Question

If $\sin \theta +\cos \theta =\sqrt{2}\cos ({90}^o-\theta )$, then find the value of $\cot \theta$.

• A. $\frac{1}{2}$
• B. $0$
• C. $\sqrt{2}-1$
• D. $\sqrt{2}$

Answer 1

The correct option is C $\sqrt{2}-1$

Given : $sin\theta +cos\theta =\sqrt{2}cos({90}^o-\theta )$

$sin\theta +cos\theta =\sqrt{2}sin\theta$......$\left(ascos\right({90}^{\circ }-\theta )=sin\theta )$

$\Rightarrow cos\theta =(\sqrt{2}-1)sin\theta$

$\Rightarrow cot\theta =\sqrt{2}-1$

Hence option ${}^{\prime }{C}^{\prime }$ is the answer.