If y=cot^{-1}(square root cosx) - tan^{-1}(square root cosx) prove that sin y= tan^{2} x/2. Share with your friends Share 26 Atul Singh answered this Please find this answer 36 View Full Answer Nishant answered this 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 -9 Aakarshee Jain answered this Is it board ppaer q -8 Khushboo answered this Yes its a board question Cbse 2013 0 Mridul answered this Answer 2 Muskan Khator answered this Please find this answer 4