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

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

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

prove

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

True

Solution steps

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

Manipulating left 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

tan (\frac{4 π}{3} - \frac{π}{4}) = 2 - 3

sec (x) + tan (x) = \frac{1}{( sec ( x ) - tan ( x ) )}

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

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

2 (sec (x) cot (x)) = 2 csc (x)

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