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Prove that (1+sinA-cosA)²/(1+sinA+cosA)²=1-cosA/1+cosA

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Prove that (1+sinA-cosA)²/(1+sinA+cosA)²=1-cosA/1+cosA

Posted by Nikita Sharma 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Sneha Singh 6 years, 10 months ago

=(1+sin²A+cos²A+2sinA-2sinA.cosA-2cosA)/(1+sin²A+cos²A+2sinA+2sinA.cosA+2cosA) = (1+1+2sinA-2sinA.cosA-2cosA)/(1+1+2sinA+2sinA.cosA+2cosA) = (2+2sinA-2sinA.cosA-2cosA)/(2+2sinA+2sinA.cosA+2cosA) = {2(1+sinA)(1-cosA)}/{2(1+sinA)(1+cosA) = 1-cosA/1+cosA

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