Question

(cosec-cot)²=1-cos÷1+cos​

Answer 1

Heya!

Here is ur answer...

To proove:

(cosecΦ - cotΦ)² = 1-cosΦ/1+cosΦ

LHS :

= (cosecΦ - cotΦ)²

= (1/sinΦ-cosΦ/sinΦ)²

= (1-cosΦ/sinΦ)²

= (1-cosΦ)²/sinΦ²

= (1-cosΦ)²/1-cos²Φ

= (1-cosΦ)(1-cosΦ) / (1+cosΦ)(1-cosΦ)

= 1-cosΦ/1+cosΦ

RHS = 1-cosΦ/1+cosΦ

Therefore, LHS = RHS

Hence proved!

Identities used:

>> CosecΦ = 1/sinΦ

>> CotΦ = cosΦ/sinΦ

>> sin²Φ = 1-cos²Φ

>> a²-b² = (a+b)(a-b)

>> (a-b)² = (a-b)(a-b)

Hope it helps u..