Question

1-tan^2 theta/1+ cot^2 theta= (1- tan theta / 1- cot theta ) ^2​

Answer 1

1-tan^2 theta/1+ cot^2 theta= (1- tan theta / 1- cot theta ) ^2

Answer 2

Correct Question :-

Prove :- (1 + tan^2A)/(1+ cot^2A) = (1- tanA/1 - cotA)²

Solution :-

LHS :-

→ (1 + tan^2A)/(1+ cot^2A)

Putting :-

• cotA = 1/tanA

→ (1 + tan^2A)/(1+ 1/tan²A)

→ (1 + tan^2A)/{(tan^2A+1)/tan²A}

→ (1 + tan²A)tan²A / (1 + tan²A)

→ tan²A .

RHS :-

→ (1- tanA/1 - cotA)²

→ (1 - tanA)² / (1 - cotA)²

using :-

• (a - b)² = a² + b² - 2ab

→ (1 + tan²A - 2tanA) / (1 + cot²A - 2cotA)

Putting :-

• cotA = 1/tanA

→ (1 + tan²A - 2tanA) / {1 + (1/tan²A) - 2(1/tanA)}

→ (1 + tan²A - 2tanA)/{(tan²A + 1 - 2tanA) / tan²A}

→ (1 + tan²A - 2tanA)tan²A/(1 + tan²A - 2tanA)

→ tan²A .

Hence,

→ LHS = RHS . (Proved).