Question

sin 3x + sin 5x / cos 3x +cos 5x= π\16
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Answer 1

Answer:

1

Step-by-step explanation:

→ (sin 3x+sin 5x) /(cos 3x+cos 5x)

→ (sin 5x + sin 3x) /(cos 5x+cos 3x)

using :-

sin C + sin D = 2 * sin(C + D/2) * cos(C - D)/2 in numerator .

cos C + cos D = 2 * cos(C + D/2) * cos(C - D)/2 in denominator .

→ [2 * sin(5x + 3x/2) * cos(5x - 3x/2)] / [2 * cos(5x + 3x/2) * cos(5x - 3x/2)]

→ [2 * sin(8x/2) * cos(2x/2)] / [2 * cos(8x/2) * cos(2x/2)]

→ (2 * sin 4x * cos x) / (2 * cos 4x * cos x)

→ sin 4x / cos 4x

using :-

tan A = sin A / cos A

→ tan 4x

putting value of x now,

→ tan 4(π/16)

→ tan (π/4)

→ tan 45°

→ 1