Question

If tan(cot x) = cot ( tan x), then sin 2x =
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Answer 1

tan (cot x) = cot (tan x)

→ tan (cot x) = tan (nπ + π/2 - tan x) {cot Ө = tan (π/2 - Ө)}

→ cot x = nπ + π/2 - tan x {both sides have same trigonometric function, thus the angles will be equal}

→ cot x + tan x = nπ + π/2

→ cos x/sin x + sin x/cos x = nπ + π/2

→ (cos² x + sin² x)/sin x cos x = nπ + π/2 {cos² Ө + sin² Ө = 1}

→ 1/sin x cos x = nπ + π/2

→ 1/sin x cos x = π (2n + 1)/2

→ 2/π(2n + 1) = sin x cos x

→ 4/π(2n + 1) = 2sin x cos x {Multiply by 2}

→ 4/π(2n + 1) = sin 2x {2sin x cos x = sin 2x}

Thus, sin 2x = 4/π(2n + 1)

Answer 2

Answer:

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