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Popular Trigonometry Problems

prove cos(B)csc(B)tan(B)=11	prove\:\cos(B)\csc(B)\tan(B)=11
prove tan(8x)=(8tan(x))/(1-tan^2(x))	prove\:\tan(8x)=\frac{8\tan(x)}{1-\tan^{2}(x)}
prove cos(2x)=5-2cos(x)	prove\:\cos(2x)=5-2\cos(x)
prove cos((3pi)/2123)=cos(pi/2123)	prove\:\cos(\frac{3π}{2}\cdot\:123)=\cos(\frac{π}{2}\cdot\:123)
prove tan(-a)=(cos(pi/2+a))/(cos(a))	prove\:\tan(-a)=\frac{\cos(\frac{π}{2}+a)}{\cos(a)}
prove (1-cos^2(x))(cot^2(x)+1)=1	prove\:(1-\cos^{2}(x))(\cot^{2}(x)+1)=1
prove sin(θ)-1/(sin(θ))=cos(θ)	prove\:\sin(θ)-\frac{1}{\sin(θ)}=\cos(θ)
prove cos^8(x)=sin^7(x)cos^1(x)	prove\:\cos^{8}(x)=\sin^{7}(x)\cos^{1}(x)
prove (cot(x)+1)^2-2cot(x)=csc^2(x)	prove\:(\cot(x)+1)^{2}-2\cot(x)=\csc^{2}(x)
prove csc(x)(2)=sin(x)(1/2)	prove\:\csc(x)(2)=\sin(x)(\frac{1}{2})
prove cos(θ)= 1/3	prove\:\cos(θ)=\frac{1}{3}
prove sec(θ)-(tan(θ))/(csc(θ))=cos(θ)	prove\:\sec(θ)-\frac{\tan(θ)}{\csc(θ)}=\cos(θ)
prove sec^2(x)=(1+tan^2(x))	prove\:\sec^{2}(x)=(1+\tan^{2}(x))
prove cot^2(x)sec^2(x)=cot^2(x)+1	prove\:\cot^{2}(x)\sec^{2}(x)=\cot^{2}(x)+1
prove (sin(x))/(cos(x)+sin(x))=1	prove\:\frac{\sin(x)}{\cos(x)+\sin(x)}=1
prove csc(2x)= 1/(2sin(x))	prove\:\csc(2x)=\frac{1}{2\sin(x)}
prove cos(x)=(cot(x))/(tan(x))	prove\:\cos(x)=\frac{\cot(x)}{\tan(x)}
prove (sec(t)-1)(sec(t)+1)=tan^2(t)	prove\:(\sec(t)-1)(\sec(t)+1)=\tan^{2}(t)
prove cos^2(2a)-sin^2(2a)=cos(4a)	prove\:\cos^{2}(2a)-\sin^{2}(2a)=\cos(4a)
prove tan(2x)-2cos(x)=0	prove\:\tan(2x)-2\cos(x)=0
prove (6cot(x))/(sec(x))=6csc(x)-6sin(x)	prove\:\frac{6\cot(x)}{\sec(x)}=6\csc(x)-6\sin(x)
prove cos^2(a)cot^2(a)=cot^2(a)-cos^2(a)	prove\:\cos^{2}(a)\cot^{2}(a)=\cot^{2}(a)-\cos^{2}(a)
prove cos(θ)= 1/2	prove\:\cos(θ)=\frac{1}{2}
prove csc(2x)= 1/(sin^2(x)-1)	prove\:\csc(2x)=\frac{1}{\sin^{2}(x)-1}
prove (1+tan^2(α))(1-sin^2(α))=1	prove\:(1+\tan^{2}(α))(1-\sin^{2}(α))=1
prove csc(θ)-cot(θ)=(1-cos(θ))/(sin(θ))	prove\:\csc(θ)-\cot(θ)=\frac{1-\cos(θ)}{\sin(θ)}
prove tan(x)=tan(x)+2sin^2(x)	prove\:\tan(x)=\tan(x)+2\sin^{2}(x)
prove 1/(2cot(1-cos^2(x)))=csc(2x)	prove\:\frac{1}{2\cot(1-\cos^{2}(x))}=\csc(2x)
prove 2cos(3x)cos(3x)=1-2sin(3x)sin(2x)	prove\:2\cos(3x)\cos(3x)=1-2\sin(3x)\sin(2x)
prove (1+csc(x))(1-csc(x))=-cot^2(x)	prove\:(1+\csc(x))(1-\csc(x))=-\cot^{2}(x)
prove cot(u)= 1/(tan(u))	prove\:\cot(u)=\frac{1}{\tan(u)}
prove-sin(2x)=-4cos(x)sin(x)	prove\:-\sin(2x)=-4\cos(x)\sin(x)
prove cos(θ)(tan(θ)-sec(-θ))=sin(θ)-1	prove\:\cos(θ)(\tan(θ)-\sec(-θ))=\sin(θ)-1
prove cos(pi/2)=-0	prove\:\cos(\frac{π}{2})=-0
prove cos(x)+1=sin(2x)	prove\:\cos(x)+1=\sin(2x)
prove ((sec^2(x)))/(sec^2(x)-1)=csc^2(x)	prove\:\frac{(\sec^{2}(x))}{\sec^{2}(x)-1}=\csc^{2}(x)
prove (sin(x))(tan(x)cos(x)-cot(x)cos(x))=1-2cos(2x)	prove\:(\sin(x))(\tan(x)\cos(x)-\cot(x)\cos(x))=1-2\cos(2x)
prove sin(20)=2cos(10)*sin(10)	prove\:\sin(20^{\circ\:})=2\cos(10^{\circ\:})\cdot\:\sin(10^{\circ\:})
prove sin^2(x)=sec(x)cos(x)-cos^2(x)	prove\:\sin^{2}(x)=\sec(x)\cos(x)-\cos^{2}(x)
prove 1-2sin^2(2θ)=8cos^4(θ)-8cos^2(θ)+1	prove\:1-2\sin^{2}(2θ)=8\cos^{4}(θ)-8\cos^{2}(θ)+1
prove sech^2(x)+tanh^2(x)=1	prove\:\sech^{2}(x)+\tanh^{2}(x)=1
prove sec(x)cos(x)-2cos^2(x)=-(cos(2x))	prove\:\sec(x)\cos(x)-2\cos^{2}(x)=-(\cos(2x))
prove 2cos^2(A)-cos(2A)-1=0	prove\:2\cos^{2}(A)-\cos(2A)-1=0
prove ((2sec(x)))/(tan(x))=2csc(x)	prove\:\frac{(2\sec(x))}{\tan(x)}=2\csc(x)
prove (cot(x)+1)/(cos(x)+sin(x))=csc(x)	prove\:\frac{\cot(x)+1}{\cos(x)+\sin(x)}=\csc(x)
prove sec^2(y)=(sec(y))^2	prove\:\sec^{2}(y)=(\sec(y))^{2}
prove csc(A)= 7/4	prove\:\csc(A)=\frac{7}{4}
prove (sin^2(x))/(sin^2(x))=sin(x)	prove\:\frac{\sin^{2}(x)}{\sin^{2}(x)}=\sin(x)
prove csc(cos(+sin(x)))=cot(+1)	prove\:\csc(\cos(+\sin(x)))=\cot(+1)
prove 4sin(x/2)cos(x/2)=2sin(x)	prove\:4\sin(\frac{x}{2})\cos(\frac{x}{2})=2\sin(x)
prove 5cos(x)-3=3cos(x)-4	prove\:5\cos(x)-3=3\cos(x)-4
prove (cos(φ)+1)/(sin(φ)+tan(φ))=cot(φ)	prove\:\frac{\cos(φ)+1}{\sin(φ)+\tan(φ)}=\cot(φ)
prove tan(x)+tan(x)=0	prove\:\tan(x)+\tan(x)=0
prove 2cos^2(x)-cos(2x)=1	prove\:2\cos^{2}(x)-\cos(2x)=1
prove-cot^2(x)=1-csc^2(x)	prove\:-\cot^{2}(x)=1-\csc^{2}(x)
prove 1/(tan(2θ))=(cot^2(θ)-1)/(2cot(θ))	prove\:\frac{1}{\tan(2θ)}=\frac{\cot^{2}(θ)-1}{2\cot(θ)}
prove (1-cos(θ))+sin^2(θ)=2	prove\:(1-\cos(θ))+\sin^{2}(θ)=2
prove 1/(sec(θ))=(sec(θ))^{-1}	prove\:\frac{1}{\sec(θ)}=(\sec(θ))^{-1}
prove sin^2(2x)= 1/(2(1-cos(4x)))	prove\:\sin^{2}(2x)=\frac{1}{2(1-\cos(4x))}
prove sin(2θ)+cos(2θ)=1	prove\:\sin(2θ)+\cos(2θ)=1
prove 25(sec^2(5x)-tan^2(5x))=25	prove\:25(\sec^{2}(5x)-\tan^{2}(5x))=25
prove cot^2(x)=((cos^2(x)))/(1-cos^2(x))	prove\:\cot^{2}(x)=\frac{(\cos^{2}(x))}{1-\cos^{2}(x)}
prove+(cos(x))/(1-sin(x))=sec(x)+tan(x)	prove\:+\frac{\cos(x)}{1-\sin(x)}=\sec(x)+\tan(x)
prove sin(A)cos(A)tan(A)=sin^2(A)	prove\:\sin(A)\cos(A)\tan(A)=\sin^{2}(A)
prove sin((4pi)/3)=sqrt(3)cos((2pi)/3)	prove\:\sin(\frac{4π}{3})=\sqrt{3}\cos(\frac{2π}{3})
prove (sin(2x)+sin(6x))/(cos(2x)-cos(6x))=cot(2x)	prove\:\frac{\sin(2x)+\sin(6x)}{\cos(2x)-\cos(6x)}=\cot(2x)
prove sin^2(x)+sin^2(θ)=1	prove\:\sin^{2}(x)+\sin^{2}(θ)=1
prove (cot(x)-sec(x))/(csc(x))=1	prove\:\frac{\cot(x)-\sec(x)}{\csc(x)}=1
prove tan^2(0)=-tan(0)	prove\:\tan^{2}(0)=-\tan(0)
prove csc(2y)=(csc(y))/(2cos(y))	prove\:\csc(2y)=\frac{\csc(y)}{2\cos(y)}
prove cos(θ-270)=-sin(θ)	prove\:\cos(θ-270^{\circ\:})=-\sin(θ)
prove 1+tan^2(x)+cot(x)=sec^2(x)+cos(x)	prove\:1+\tan^{2}(x)+\cot(x)=\sec^{2}(x)+\cos(x)
prove cos(θ)sec(θ)=tan(θ)cot(θ)	prove\:\cos(θ)\sec(θ)=\tan(θ)\cot(θ)
prove cos(x)-cos(x)=2cos(x)	prove\:\cos(x)-\cos(x)=2\cos(x)
prove (cos^2(2θ))/2 =(1+cos(4θ))/8	prove\:\frac{\cos^{2}(2θ)}{2}=\frac{1+\cos(4θ)}{8}
prove (cos^2(x))/(sin^2(x))+1=csc^2(x)	prove\:\frac{\cos^{2}(x)}{\sin^{2}(x)}+1=\csc^{2}(x)
prove 1/(csc(x))+1= 1/(sin(x))+1	prove\:\frac{1}{\csc(x)}+1=\frac{1}{\sin(x)}+1
prove (sin(2θ))(tan(θ))+cos(2θ)=1	prove\:(\sin(2θ))(\tan(θ))+\cos(2θ)=1
prove cot(x)-cot(x)cos^2(x)=sin(x)cos(x)	prove\:\cot(x)-\cot(x)\cos^{2}(x)=\sin(x)\cos(x)
prove cot^2(θ)=(csc^2(θ))/(sec^2(θ))	prove\:\cot^{2}(θ)=\frac{\csc^{2}(θ)}{\sec^{2}(θ)}
prove 1/(sec(θ))=arcsec(θ)	prove\:\frac{1}{\sec(θ)}=\arcsec(θ)
prove ((cot(x)))/((csc(x)))=cos(x)	prove\:\frac{(\cot(x))}{(\csc(x))}=\cos(x)
prove (1+cot^2(x))/(cot^2(x))=sec^2(x)	prove\:\frac{1+\cot^{2}(x)}{\cot^{2}(x)}=\sec^{2}(x)
prove sec^2(x)-tan^2(x)=sec(x)cos(x)	prove\:\sec^{2}(x)-\tan^{2}(x)=\sec(x)\cos(x)
prove cos^2(4x)= 1/2+1/2 cos(16x)	prove\:\cos^{2}(4x)=\frac{1}{2}+\frac{1}{2}\cos(16x)
prove-3sin(35)-3sin(15)=-6sin(25)cos(10)	prove\:-3\sin(35)-3\sin(15)=-6\sin(25)\cos(10)
prove ((sec^2(t)))/(sec^2(t)-1)=csc^2(t)	prove\:\frac{(\sec^{2}(t))}{\sec^{2}(t)-1}=\csc^{2}(t)
prove sin^2(x)=cos(2x)+2	prove\:\sin^{2}(x)=\cos(2x)+2
prove 1+cos^2(x)=2-sin^2(x)	prove\:1+\cos^{2}(x)=2-\sin^{2}(x)
prove sin((3pi)/2+0)=-cos(0)	prove\:\sin(\frac{3π}{2}+0)=-\cos(0)
prove sin^2(x)=cos(2x)-2	prove\:\sin^{2}(x)=\cos(2x)-2
prove (tan(θ)cot(θ))/(cos(θ))=sec(θ)	prove\:\frac{\tan(θ)\cot(θ)}{\cos(θ)}=\sec(θ)
prove 2(cos(θ-1))^2=cos^4(θ)-sin^4(θ)	prove\:2(\cos(θ-1))^{2}=\cos^{4}(θ)-\sin^{4}(θ)
prove (sec^2(x/2))/2 = 1/(1+cos(x))	prove\:\frac{\sec^{2}(\frac{x}{2})}{2}=\frac{1}{1+\cos(x)}
prove cos(x)= 15/17	prove\:\cos(x)=\frac{15}{17}
prove tan(b)+cot(b)= 1/(sin(b)cos(b))	prove\:\tan(b)+\cot(b)=\frac{1}{\sin(b)\cos(b)}
prove csc(A)-sin(A)=(cos(A))(cot(A))	prove\:\csc(A)-\sin(A)=(\cos(A))(\cot(A))
prove (cos^2(x))/(cos^2(x))=1	prove\:\frac{\cos^{2}(x)}{\cos^{2}(x)}=1
prove ((tan(x)cot(x)))/(sec(x))=cos(x)	prove\:\frac{(\tan(x)\cot(x))}{\sec(x)}=\cos(x)
prove sec(b)cot(b)=csc(b)tan(b)	prove\:\sec(b)\cot(b)=\csc(b)\tan(b)

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