QJEEM21Ma88e3: JEE Main 2021 Mathematics - Class 11 JEEM21Ma88e3 Solution: If 0 < x, y < and cosx + cosy cos(x + y) = , then sinx + cosy…

Question

Verified Solution • 2025–26 Session moderate

If 0 < x, y <

\pi

and cosx + cosy

-

cos(x + y) =

{3 \over 2}

, then sinx + cosy is equal to :

Accepted Answer

2\cos \left( {{{x + y} \over 2}} \right)\cos \left( {{{x - y} \over 2}} \right) - \left[ {2{{\cos }^2}\left( {{{x + y} \over 2}} \right) - 1} \right] = {3 \over 2}

2\cos \left( {{{x + y} \over 2}} \right)\left[ {\cos \left( {{{x - y} \over 2}} \right) - \cos \left( {{{x + y} \over 2}} \right)} \right] = {1 \over 2}

2\cos \left( {{{x + y} \over 2}} \right)\left[ {2\sin \left( {{x \over 2}} \right).\sin \left( {{y \over 2}} \right)} \right] = {1 \over 2}

\cos \left( {{{x + y} \over 2}} \right).\sin \left( {{x \over 2}} \right).\sin \left( {{y \over 2}} \right) = {1 \over 8}

Possible when

{x \over 2} = 30^\circ

&

{y \over 2} = 30^\circ

x = y = 60^\circ

\sin x + \cos y = {{\sqrt 3 } \over 2} + {1 \over 2} = {{\sqrt 3 + 1} \over 2}

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