If $$U=$$$$cot$$−$$1$$⁡$$cos$$⁡$$2$$θ−$$tan$$−$$1$$⁡$$cos$$⁡$$2$$θ, then $$sin$$ U equals

Question

If $$U=$$$$cot$$−$$1$$⁡$$cos$$⁡$$2$$θ−$$tan$$−$$1$$⁡$$cos$$⁡$$2$$θ, then $$sin$$ U equals

Infinity Learn · Accepted Answer

We have,$$U=$$$$cot$$−$$1$$⁡$$cos$$⁡$$2$$θ−$$tan$$−$$1$$⁡$$cos$$⁡$$2$$θ⇒ $$U=$$π$$2$$−$$tan$$−$$1$$⁡$$cos$$⁡$$2$$θ−$$tan$$−$$1$$⁡$$cos$$⁡$$2$$θ⇒ $$U=$$π$$2$$−$$2tan$$−$$1$$⁡$$cos$$⁡$$2$$θ⇒ $$U=$$π$$2$$−$$tan$$−$$1$$⁡$$2cos$$⁡$$2$$θ$$1$$−$$cos$$⁡$$2$$θ⇒ $$U=$$π$$2$$−$$tan$$−$$1$$⁡$$cos$$⁡$$2$$θ$$sin2$$⁡θ⇒ $$tan$$⁡π$$2$$−$$U=$$$$cos$$⁡$$2$$θ$$sin2$$⁡θ⇒ $$cot$$⁡$$U=$$$$cos$$⁡$$2$$θ$$sin2$$⁡θ⇒ $$sin$$⁡$$U=11+cot2$$⁡θ$$=11+$$$$cos$$⁡$$2$$θ$$sin4$$⁡θ⇒ $$sin$$⁡$$U=sin2$$⁡θ$$sin4$$⁡θ$$+1$$−$$2sin2$$⁡θ⇒ $$sin$$⁡$$U=sin2$$⁡θ$$1$$−$$sin2$$⁡θ$$=tan2$$⁡θ

If $U = \cot^{- 1} \sqrt{\cos 2 θ} - \tan^{- 1} \sqrt{\cos 2 θ}$ , then $\sin U$ equals

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If U=cot−1⁡cos⁡2θ−tan−1⁡cos⁡2θ, then sin U equals

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If $U = \cot^{- 1} \sqrt{\cos 2 θ} - \tan^{- 1} \sqrt{\cos 2 θ}$ , then $\sin U$ equals