If $$cos$$−$$1$$⁡$$p+$$$$cos$$−$$1$$⁡$$1$$−$$p+$$$$cos$$−$$1$$⁡$$1$$−$$q=3$$$$π$$$$2$$, then the value of q is

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If $$cos$$−$$1$$⁡$$p+$$$$cos$$−$$1$$⁡$$1$$−$$p+$$$$cos$$−$$1$$⁡$$1$$−$$q=3$$$$π$$$$2$$, then the value of q is

Infinity Learn · Accepted Answer

Let α$$=$$$$cos$$−$$1$$⁡p,β$$=$$$$cos$$−$$1$$⁡$$1$$−pand γ$$=$$$$cos$$−$$1$$⁡$$1$$−q or $$cos$$⁡α$$=p$$,$$cos$$⁡β$$=1$$−pand $$cos$$⁡γ$$=1$$−qTherefore, $$sin$$⁡α$$=1$$−p,$$sin$$⁡β$$=p$$,$$sin$$⁡γ$$=qThe$$ given equation may be written as α$$+$$β$$+$$γ$$=3$$$$π$$$$4or$$ α$$+$$β$$=3$$$$π$$$$4$$−γ or $$cos$$⁡$$($$α$$+$$β$$)=$$$$cos$$⁡$$3$$$$π$$$$4$$−γ⇒$$cos$$⁡α$$cos$$⁡β−$$sin$$⁡γ$$sin$$⁡β$$=$$$$cos$$⁡[π−$$($$π$$/4+$$γ$$)$$]$$=$$−$$cos$$⁡π$$4+$$γ⇒$$p1$$−p−$$1$$−$$pp=$$−$$121$$−q−$$12q$$ ⇒$$0=1$$−q−q⇒$$1$$−$$q=q$$⇒$$q=12$$

If $\cos^{- 1} \sqrt{p} + \cos^{- 1} \sqrt{1 - p} + \cos^{- 1} \sqrt{1 - q} = \frac{3 π}{2}$ , then the value of q is

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If cos−1⁡p+cos−1⁡1−p+cos−1⁡1−q=3π2, then the value of q is

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If $\cos^{- 1} \sqrt{p} + \cos^{- 1} \sqrt{1 - p} + \cos^{- 1} \sqrt{1 - q} = \frac{3 π}{2}$ , then the value of q is