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(1) 1/seca-tana – 1/cosa = 1/cosa-1/seca+tana (ii) 1/secA +1/secA+1= 2cosecAcot A |
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Answer» LHS=1/seca-tana – 1/cosa = cosa /(1- sina) – 1/cosa = (cos^2a – (1 – sina))/(1 – sina)(cosa) = (sina – sin^2a)/(1 – sina)(cosa) = (sina)(1 – sina)/(1 – sina)(cosa) = tanaRHS=1/cosa – 1/(seca+tana) = (1/cosa) –( cosa/(sina+1)) = (sina +1 – cos^2a)/(cosa)(sina+1) = (sina +1 +sin^2a – 1)/(sina+1)(cosa) = sina/cosa = tana [1/(SecA-1)]+[1/(SecA+1)] =[1*(SecA+1) + 1*(SecA-1)]/[(SecA-1)(SecA+1)] =[SecA + 1 + SecA - 1]/[Sec^2A - 1^2] =[SecA + 1 + SecA - 1]/[Tan2A][Using: Sec2Θ-Tan2Θ=1 => Sec2Θ-1=Tan2Θ] =[SecA +1+ SecA -1]/[Tan^2A] =[2SecA]/[Tan^2A] =[2(1/CosA)]/[(Sin^2A/Cos^2A)] =[(2*1)/CosA]*[Cos^2A/Sin^2A] = [2/CosA] * [Cos^2A/Sin^2A] = [2] * [CosA/Sin^2A] = 2*(CosA/SinA)*(1/SinA) = 2CotACosecA |
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