The general value of θ obtained from the equation cos 2θ = sin α is

1.	The general value of θ obtained from the equation cos 2θ = sin α is (a) θ = 2nπ ± \(\big(\) \(\frac{π}{2}\) - α \(\big)\)(b) θ = \(\frac{nπ +(-1)^n\alpha}{2}\) (c) θ = nπ ± \(\big(\) \(\frac{π}{4}\) - \(\frac{α}{2}\) \(\big)\)(d) 2θ = \(\frac{π}{2}\) – α
Answer» Answer : (c) = θ = nπ ± \(\big( \frac{\pi}{4} -\frac{\alpha}{2}\big)\) cos 2θ = sin α ⇒ cos 2θ = cos \(\big( \frac{\pi}{2} -\alpha\big)\) ⇒ 2θ = 2nπ ± \(\big( \frac{\pi}{2} -\alpha\big)\) (∵ cos θ = cos α ⇒ θ = 2nπ ± α) ⇒ θ = nπ ± \(\big( \frac{\pi}{4} -\frac{\alpha}{2}\big)\)

The general value of θ obtained from the equation cos 2θ = sin α is (a) θ = 2nπ ± \(\big(\) \(\frac{π}{2}\) - α \(\big)\)(b) θ = \(\frac{nπ +(-1)^n\alpha}{2}\) (c) θ = nπ ± \(\big(\) \(\frac{π}{4}\) - \(\frac{α}{2}\) \(\big)\)(d) 2θ = \(\frac{π}{2}\) – α

Answer»

Answer : (c) = θ = nπ ± \(\big( \frac{\pi}{4} -\frac{\alpha}{2}\big)\)

cos 2θ = sin α ⇒ cos 2θ = cos \(\big( \frac{\pi}{2} -\alpha\big)\)

⇒ 2θ = 2nπ ± \(\big( \frac{\pi}{2} -\alpha\big)\) (∵ cos θ = cos α ⇒ θ = 2nπ ± α)

⇒ θ = nπ ± \(\big( \frac{\pi}{4} -\frac{\alpha}{2}\big)\)