Question

If sin x = cos² x, then write the value of cos² x (1 + cos² x).

 

Answer 1

We have: 
\[\sin x = \cos^2 x \left( 1 \right)\]
\[ \therefore \cos^2 x \left( 1 + \cos^2 x \right)\]
\[ = \sin x\left( 1 + \sin x \right) \left[\text{ Using }\left( 1 \right) \right]\]
\[ = \sin x + \sin^2 x\]
\[ = \sin x + 1 - \cos^2 x\]
\[ = \sin x + 1 - \sin x \left[\text{ Using }\left( 1 \right) \right]\]
\[ = 1\]