If cosecx – sinx = a 3 , secx – cosx = b 3 , then prove that a 2 b 2 (a 2 + b 2 ) = 1.

Question

Philoid · Accepted Answer

Given cosecx – sinx = a³

We know that cosecx = 1/ sinx.

We know that 1 – sin²x = cos²x

… (1)

Also given secx – cosx = b³

We know that secx = 1/ cosx

We know that 1 – cos²x = sin²x

… (2)

Consider LHS = a²b² (a² + b²)

We know that cos² + sin²x = 1

= 1

= RHS

Hence proved.