Question

Cotx/cosec x-1 = ✓1+sin x /1-sin x

Answer 1

Answer:

QED

Step-by-step explanation:

Cotx/(cosec x-1) = ✓1+sin x /1-sin x

cotx = cosx/Sinx   & Cosec x = 1/Sinx

=>  (cosx/Sinx) /(1/Sinx - 1) = ✓((1+sin x) /(1-sin x))

=> (Cosx/Sinx)/((1 - Sinx)/Sinx) =✓((1+sin x) /(1-sin x))

Cancelling Sinx

=>  Cosx/(1 - Sinx) = ✓((1+sin x) /(1-sin x))

as we know that Cos²x = 1 - Sin²x

=> Cosx = √(1 - Sin²x)

=> Cosx = √(1+sinx)(1-Sinx)

1-Sinx = √(1-Sinx)×√(1-Sinx)

putting these values

=> (√(1+sinx)(1-Sinx)) / (√(1-Sinx)×√(1-Sinx)) = ✓((1+sin x) /(1-sin x))

cancelling √(1-Sinx)

=>  √(1+sinx) / √(1-Sinx) = ✓((1+sin x) /(1-sin x))

=> √((1+sinx) /(1-Sinx)) = ✓((1+sin x) /(1-sin x))

=> LHS = RHS

QED