Question

Attention!!!


Prove it :


(CosecØ-cotØ)² = (1-cosØ)/(1+cosØ)​

Answer 1

Answer:

hope this helps u.....

Answer 2

$\color{blue}\huge\underline\mathfrak{Solution:-}$

Taking LHS,

(CosecØ-cotØ)²

=> [(1/sinØ) - (cosØ/sinØ)]²

=> [(1-cosØ)/sinØ]²

=> (1-cosØ)²/sin²Ø

Taking RHS,

(1-cosØ)/(1+cosØ)

Rationalise it :

=> [(1-cosØ)(1-cosØ)]\[(1+cosØ)(1-cosØ)

=> (1-cosØ)²/(1-cos²Ø) [ a²-b² = (a+b)(a-b) ]

=> (1-cosØ)²/sin²Ø

LHS = RHS

Hence proved!

___________________________

$\large\underline\bold\red{Identity\:used:-}$

★ 1 - cos²Ø = sin²Ø

$\large\underline\bold\red{Trigonometrical\:Ratios\:used:-}$

★ cosecØ = 1/sinØ

★ cotØ = cosØ/sinØ