Question

If cosecx – sinx = a³, secx – cosx = b³, then prove that a² b² (a² + b²) = 1.

Answer 1

Given cosec x – sin x = a³

We know that cosec x = 1/ sin x.

We know that 1 – sin²x = cos²x

Also given secx – cosx = b³

We know that sec x = 1/ cos x

We know that 1 – cos²x = sin²x

Consider LHS = a²b² (a² + b²)

We know that cos² x+ sin²x = 1

= 1

= RHS

Hence proved.