If y=cot-1(square root cosx) - tan-1(square root cosx)

prove that sin y= tan2 x/2.

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Y= cot-¹( √cosx ) - tan-¹( √cosx) Let cot-¹(√cosx) =P cotP = √cosx sinP = 1/√(1 + cosx) P = sin-¹{1/√(1 + cosx)} Let tan-¹( √cosx) = Q tanQ = √cosx sinQ = √cosx/√(1 + cosx) Q = sin-¹( √cosx/√(1 + cosx ) y = P - Q siny = sin(P - Q ) = sinP.cosQ - cosP.sinQ = 1/√(1 + cosx).1/√(1 + cosx) - √cosx/√(1 + cosx) .√cosx/√(1 + cosx) = (1 - cosx)/(1 + cosx) = 2sin²x/2/2cos²x/2 = tan²x/2 Hence, siny = tan²x/2
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Is it board ppaer q
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Yes its a board question
Cbse 2013
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