Is cos(x)=cos^3(x)+cos(x)sin^2(x) ?

The answer to whether cos(x)=cos^3(x)+cos(x)sin^2(x) is True

Popular >

prove cos(x)=cos^3(x)+cos(x)sin^2(x)

prove

cos (x) = cos^{3} (x) + cos (x) sin^{2} (x)

True

Solution steps

cos (x) = cos^{3} (x) + cos (x) sin^{2} (x)

Manipulating right side

cos^{3} (x) + cos (x) sin^{2} (x)

Factor

cos^{3} (x) + cos (x) sin^{2} (x) : cos (x) (cos^{2} (x) + sin^{2} (x))

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

Rewrite using trig identities

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

csc (x) - sin (x) = \frac{cot ^{2} ( x )}{csc ( x )}

\frac{cot ( 2 θ )}{cos ( 2 θ )} = csc (2 θ)

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

sec^{2} (x) = (sec (x))^{2}

cos^{3} (θ) + cos (θ) sin^{2} (θ) = cos (θ)

Is cos(x)=cos^3(x)+cos(x)sin^2(x) ?
The answer to whether cos(x)=cos^3(x)+cos(x)sin^2(x) is True