Question

sin 5x + sin 3x ÷ cos 5x + cos 3x = tan 4x prove that
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Answer 1

answer:-

step by step explain

Answer 2

Solution :-

→ (sin 5x + sin 3x) / (cos 5x + cos 3x) = tan 4x

using :-

• sin A + sin B = 2•sin(A + B/2)•cos(A-B/2) in numerator .
• cos A + cos B = 2•cos(A + B/2)•cos(A-B/2) in denominator .

→ [2•sin(5x + 3x/2)•cos(5x-3x/2)] / [2•cos(5x + 3x/2)•cos(5x-3x/2)] = tan 4x

→ (2•sin 4x • cos x) / (2• cos 4x • cos x) = tan 4x

→ sin 4x / cos 4x = tan 4x

using :-

• sin x / cos x = tan 4x

→ tan 4x = tan 4x (proved.)

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