Question

Verify the identity...
csc x cos x= (1 - sin^2 x)/ sin x cos x​

Answer 1

Explanation:

`\csc x \: \cos x = \frac{1 - { \sin}^(2)x }{ \sin x \: cos x} \\ \\ rhs = \frac{1 - { \sin}^(2)x }{ \sin x \: cos x} \\ \\ = \frac{ { \cos}^(2) x}{ \sin x \: cos x} \\ \\ = \frac{ { \cos} x}{ \sin x} \\ \\ = \frac{ { 1} }{ \sin x} * \cos \\ \\ = \csc x \: \cos x \\ \\ = lhs \\ hence \: proved \\`