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Question

Prove that:
1. sec2A+cosec2A = tanA + cotA

2. sin2A(1+cot2A)+cos2A(1+tan2A) = 2

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Solution

1. LHS = 1+tan2A+1+cot2A

= tan2A+cot2A+2 = tan2A+cot2A+tanA.cotA

= (tanA+cotA)2 = tanA + cotA = R.H.S

2. L.H.S = sin2A(1+cot2A)+cos2A(1+tan2A) = sin2A+cos2A + cos2A+sin2A = 2


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