Question

PROVE THAT
COSA.Cor A ₂ 1 + cosec A A
1- SinA​

Answer 1

Step-by-step explanation:

To prove, (cosec A - 1) /(cosec A + 1) =[(cos A)/(1 + sin A)]²

L.H.S. = (cosec A - 1) /(cosec A + 1)

=(1/sin A - 1)/(1/sin A + 1) [Since from trigonometry we know cosec A = 1/sin A]

= [(1-sinA)/sin A] /[(1+sinA)/sin A] which on cancellation of the factor sin A

= (1-sinA)/(1+sin A)

which on multiplying the numerator and denominator by (1+sin A)

= (1-sinA)(1+sin A)/(1+sin A)(1+sin A)= (1-sin² A)/(1+sin A)² [∵(a-b)(a+b) = a² - b²]

= cos²A / (1 + sin A)² = (cos A)²)/(1 + sin A)²

=[(cos A)/(1 + sin A)]² = R.H.S. (Proved)