Is cos^2(x)tan(x)cot(x)=1-sin^2(x) ?

The answer to whether cos^2(x)tan(x)cot(x)=1-sin^2(x) is True

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prove cos^2(x)tan(x)cot(x)=1-sin^2(x)

prove

cos^{2} (x) tan (x) cot (x) = 1 - sin^{2} (x)

True

Solution steps

cos^{2} (x) tan (x) cot (x) = 1 - sin^{2} (x)

Manipulating left side

cos^{2} (x) tan (x) cot (x)

Express with sin, cos

cos^{2} (x) cot (x) tan (x)

Use the basic trigonometric identity:

cot (x) = \frac{cos ( x )}{sin ( x )}

= cos^{2} (x) \frac{cos ( x )}{sin ( x )} tan (x)

Use the basic trigonometric identity:

tan (x) = \frac{sin ( x )}{cos ( x )}

= cos^{2} (x) \frac{cos ( x )}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Simplify

cos^{2} (x) \frac{cos ( x )}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )} : cos^{2} (x)

cos^{2} (x) \frac{cos ( x )}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{cos ( x ) sin ( x ) cos ^{2} ( x )}{sin ( x ) cos ( x )}

Cancel the common factor:

cos (x)

= \frac{sin ( x ) cos ^{2} ( x )}{sin ( x )}

Cancel the common factor:

sin (x)

= cos^{2} (x)

= cos^{2} (x)

= cos^{2} (x)

Rewrite using trig identities

cos^{2} (x)

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

cos^{2} (x) = 1 - sin^{2} (x)

= 1 - sin^{2} (x)

= 1 - sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ( x )}{1 - cos ( x )} = cot (x) + csc (x)

tan (3 0^{\circ}) = \frac{sin ( 3 0 ^{\circ} )}{cos ( 3 0 ^{\circ} )}

\frac{1}{cos ( x ) sin ( x )} = csc (x) sec (x)

tan (2 x) - sin (2 x) = tan (2 x) sin (2 x)

tan^{2} (x) + sec^{2} (x) = 1

Is cos^2(x)tan(x)cot(x)=1-sin^2(x) ?
The answer to whether cos^2(x)tan(x)cot(x)=1-sin^2(x) is True