If then find the value of

If m sin θ = n sin (θ + 2α), then prove that

tan (θ + α) cot α =

[Hints: Express and apply componendo and dividend]

If where α lie between 0 and π/4, find value of tan 2α

[Hint: Express tan 2α as tan (α + β + α – β]

Prove that

[Hint: Express L.H.S.

If a cos θ + b sin θ = m and a sin θ – b cos θ = n, then show that a² + b² = m² + n².