Question
Class 11MathematicsTrigonometric Functions

Prove: (tan 5θ + tan 3θ) / (tan 5θ − tan 3θ) = 4 cos 2θ · cos 4θ

Verified Answer

LHS = (tan 50° + tan 30°) / (tan 50° − tan 30°)

= (sin 50°/cos 50° + sin 30°/cos 30°) / (sin 50°/cos 50° − sin 30°/cos 30°)

= (sin 50° cos 30° + sin 30° cos 50°) / (sin 50° cos 30° − sin 30° cos 50°)

= sin(50° + 30°) / sin(50° − 30°)

= sin 80° / sin 20°

= sin(2 × 40°) / sin 20°

= (2 sin 40° cos 40°) / sin 20°

= (4 sin 20° cos 20° cos 40°) / sin 20°

= 4 cos 20° cos 40° = RHS