Question

Prove That
Tan^2 A/ Tan^2 A-1+Cosec^A/Sec^2A-Cosec^2A =1/1-2Cosec^2A

Answer 1

Correct Question

Prove that tan²A/(tan²A - 1) + cosec²A/(sec²A - cosec²A) = 1/(2sin²A - 1).

Proof

L.H.S → tan²A/(tan²A - 1) + cosec²A/(sec²A - cosec²A)

→ (sin²A/cos²A)/(sin²A/cos² - 1) + (1/sin²A)/(1/cos²A - 1/sin²A)

→ (sin²A/cos²A)/(sin²A - cos²A)/cos²A + (1/sin²A)/(sin²A - cos²A)/cos²A sin²A

→ sin²A/cos²A × cos²A/(sin²A - cos²A) + 1/sin²A × cos²Asin²A/(sin²A - cos²A)

→ sin²A/(sin²A - cos²A) + cos²A/(sin²A - cos²A)

→ (sin²A + cos²A)/(sin²A - cos²A)

→ 1/(sin²A - 1 + sin²)

→ 1/(2sin² - 1) = R.H.S

Hence Proved