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$I f α, β a r e s o l u t i o n s o f \sin^{2} x + a \sin x + b = 0 a n d \cos^{2} x + c \cos x + d = 0$ , then $\sin (α + β)$ is equal to

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2aca2+c2

a2+c22ac

2bdb2+d2

b2+d22bd

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detailed solution

Correct option is A

We have sinα+sinβ=-a, cosα+cosβ=-c ⇒sinα+sinβcosα+cosβ=ac ⇒2sinα+β2cosα-β22cosα+β2cosα-β2=ac ⇒tanα+β2=ac Now sinα+β=2tanα+β21+tan2α+β2=2aca2+c2

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If α,β are solutions of sin2x+asinx+b=0 and cos2x+c cosx+d=0 , then sinα+β is equal to

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$I f α, β a r e s o l u t i o n s o f \sin^{2} x + a \sin x + b = 0 a n d \cos^{2} x + c \cos x + d = 0$ , then $\sin (α + β)$ is equal to