Q229 / 270 · NDA 2011 (Phase 2) · Mathematics

If $\sin \theta=\cos ^2 \theta$, then what is $\cos ^2 \theta\left(1+\cos ^2 \theta\right)$ equal to?

  • Correct answer
    A
    $1$
  • B
    $0$
  • C
    $\cos ^2 \theta$
  • D
    $2 \sin \theta$

Solution

$\because \begin{aligned} \because \sin \theta & =\cos ^2 \theta \\ \cos ^2 \theta\left(1+\cos ^2 \theta\right) & =\sin \theta(1+\sin \theta)\end{aligned}$ $\begin{aligned} & =\sin \theta+\sin ^2 \theta \\ & =\cos ^2 \theta+\sin ^2 \theta\end{aligned}$ $=1 \quad\left[\because \sin \theta=\cos ^2 \theta\right]$

Hence, the correct answer is option: 'A'.

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