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24. Prove that (1-sine+cosθ)2-2 (1-cos0)(1-sin0) |
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Answer» Consider the LHS:(1-sinA+cosA)^2= [(1-sinA) + cosA]^2= (1-sinA)^2+ cos^2A+ 2(1-sinA)cosA= 1 + sin^2A− 2sinA+ cos^2A+ 2(1-sinA)cosA= 1 + (sin^2A+ cos^2A)− 2sinA+ 2(1-sinA)cosA= 1 + 1− 2sinA+ 2(1-sinA)cosA [Since,sin^2A+ cos^2A =1]= 2− 2sinA+ 2(1-sinA)cosA= 2(1− sinA) + 2(1-sinA)cosA= 2(1− sinA)(1 +cosA)= RHS Like my answer if you find it useful! |
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