1.

i. i? = con"(/cosi-tan-loss), then prove that : siny = un-

Answer»

Y= cot-¹( √cosx ) - tan-¹( √cosx) Let cot-¹(√cosx) =PcotP = √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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