Question

If $(sin\theta +cos\theta )=\sqrt{2}cos\theta ,$ show that $cot\theta =(\sqrt{2}+1)$.

Answer 1

$sin\theta +cos\theta =\sqrt{2}cos\theta \Rightarrow sin\theta =(\sqrt{2}-1)cos\theta \Rightarrow \frac{sin\theta }{\sqrt{2}-1}=cos\theta \Rightarrow \frac{sin\theta (\sqrt{2}+1)}{2-1}=cos\theta \Rightarrow \frac{cos\theta }{sin\theta }=\sqrt{2}+1\therefore cot\theta =\sqrt{2}+1$