prove the question 1 -cos A/1+cosA = (cot A - cosec A) ppower2
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Step-by-step explanation:
1-cosA/1+cosA
=1-cosA/1+cosA×1-cosA/1-cosA
=(1-cosA)²/1-cos²A
=1-2cosA+cos²A/sin²A
=1/sin²A-2cosA/sin²A+cos²A/sin²A
=cosec²A-2×1/sin²A.cosA/sinA+cot²A
=cosec²A-2cosecAcotA+cot²A
=(cosecA-cotA)²
={-(cotA-cosecA)}²
=(cotA-cosec)²
=RHS. (proved)
or
(cotA-cosecA)²
={-(cscA-cotA)}²
=(cscA-cotA)²
=(1/sinA-cosA/sinA)²
=(1-cosA/sinA)²
=(1-cosA)²/sin²A
=(1-cosA)(1-cosA)/1-cos²A
=(1-cosA)(1-cosA)/(1+cosA)(1-cosA)
=1-cosA/1+cosa
=LHS. (proved)
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