Question

If A = 60° and B = 30°, verify that : sin (A + B) = sin A cos B + cos A sin B

Prove that : tan θ/(1 − cot θ) + cot θ/(1 − tan θ) = 1 + sec θ cosec θ

If a sec θ + b tan θ = m and b sec θ + a tan θ = n, prove that a² + n² = b² + m²

Use the identity : sin²A + cos²A = 1 to prove that tan²A + 1 = sec²A. Hence, find the value of tan A, when sec A = 5/3, where A is an acute angle.