secxtanx =-cscxcotx

Question

Can you solve this identity?

Answer 1

Sec x tan x = - csc x cot x

Left hand side identity = Sec x tan x

=  1 / cos x * ( sin x / cos x ) 

= sin x / cos ² x

Left hand side identity = sin x / cos ² x

Right hand side identity = - csc x cot x

=  - 1 / sin x * (cos x / sin x ) 

= - cos x / sin ² x

Right hand side identity = -  cos x / sin ² x

Left hand side identity  = Right hand side identity

sin x /cos ² x  =  - cos x / sin ² x

sin ³ x = - cos ³ x 

But sin ³ x ≠ - cos ³ x

Therefore Sec x tan x ≠ - csc x cot x .