Question

prove the following identity : cosec X - cos2 X .cosec X =1​

Answer 1

Answer:

1

$cosec \: x - cos {}^{2} x \times cosec \: x = 1$

LHS-

$cosec \: x \: - 1 - sin {}^{2} \times cosec$

$\frac{1}{sin} - 1 - sin {}^{2} \times \frac{1}{sin}$

$\frac{1 - sin - sin {}^{3} }{sin} \times \frac{1}{sin}$

$\frac{1 - sin {}^{2} }{sin} \times \frac{1}{sin}$

$\frac{cos {}^{2} }{sin} \times \frac{1}{sin}$

$\frac{cos {}^{2} }{sin {}^{2} }$

$\frac{cos {}^{2} }{1 - cos {}^{2} }$

cos and cos will cutted

ans =1