Question

prove the following Identity

(cosec A - Cot A)² = 1 - cosA
1 + cosA​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{\big(cosec(A)-cot(A)\big)^2}$

$\tt{=\left(\dfrac{1}{sin(A)}-\dfrac{cos(A)}{sin(A)}\right)^2}$

$\tt{=\left(\dfrac{1-cos(A)}{sin(A)}\right)^2}$

$\tt{=\dfrac{\big(1-cos(A)\big)^2}{sin^2(A)}}$

$\tt{=\dfrac{\big(1-cos(A)\big)\big(1-cos(A)\big)}{1-cos^2(A)}}$

$\tt{=\dfrac{\big(1-cos(A)\big)\big(1-cos(A)\big)}{\big(1-cos(A)\big)\big(1+cos(A)\big)}}$

$\tt{=\dfrac{1-cos(A)}{1+cos(A)}}$