If the sinθ + cosθ =\(\sqrt{5}\) sin(90°-θ), then find the value of cotθ.
Answer & explanation
Correct answer: option 2
sinθ + cosθ =\(\sqrt{5}\)cosθ (sin(90°-θ) = cosθ)
sinθ =\(\sqrt{5}\)cosθ - cosθ
sinθ =cosθ(\(\sqrt{5}-1\))
\(\frac{cosθ}{sinθ}\) = \(\frac{1}{\sqrt {5}-1}\)
cotθ = \(\frac{\sqrt {5}+1}{4}\) (By rationalisation)