Question

Prove that

$\frac{1 + {cos}^{2} a }{ { \sin }^{2} a} = 2 {cosec}^{2} a - 1$


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Answer 1

(1 + cos²a) / sin²a = 2cosec²a - 1

L.H.S. ↓

(1 + cos²a) / sin²a

• cos²A = 1 - sin²A

1 + (1-sin²A)/sin²A

(2 - sin²A)/(sin²A)

(2/sin²A) - (sin²A/sin ²A)

2cosec²A - 1

RHS ↑