Question

Prove that (cosec a + cot a)^2 =sec a + 1/ sec a - 1

Answer 1

LHS = (cosecA+cotA)²

= [1/sinA + cosA/sinA]²

= (1/sin²A)[1+cosA]²

= (1/sin²A)[1+1/secA]²

= (1/sin²A)[(secA+1)/secA]²

= (1/sin²Asec²A)(secA+1)²

= (1/tan²A)(secA+1)²

= (secA+1)²/(sec²A-1)

= (secA+1)²/[(secA+1)(secA-1)]

= (secA+1)/(secA-1)

= RHS

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