Question

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

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}: \\ \sin x={\cos }^{2}x\left(1\right) \\ \therefore {\cos }^{2}x\left(1+{\cos }^{2}x\right) \\ =\sin x\left(1+\sin x\right)\left[\mathrm{Using}\left(1\right)\right] \\ =\sin x+{\sin }^{2}x \\ =\sin x+1-{\cos }^{2}x \\ =\sin x+1-\sin x\left[\mathrm{Using}\left(1\right)\right] \\ =1 \end{gathered}$$