Question

2tan⁻¹(cosx) = tan⁻¹(2cosecx),Solve it.

Answer 1

Solution :

Now, 2 tan⁻¹(cosx) = tan⁻¹(2 cosecx)

⇒ tan⁻¹{2 cosx/(1 - cos²x)} = tan⁻¹(2/sinx)

⇒ 2 cosx/sin²x = 2/sinx

⇒ cosx/sinx * 1/sinx = 1/sinx

⇒ cotx/sinx = 1/sinx

⇒ cotx sinx = sinx

⇒ cotx sinx - sinx = 0

⇒ sinx (cotx - 1) = 0

∴ either sinx = 0 or, cotx - 1 = 0

⇒ sinx = 0 or, cotx = 1

⇒ sinx = sin0 or, cotx = cot(π/4)

⇒ x = 0 or, x = π/4

∴ the required solution is

x = 0 , π/4

Answer 2

Answer:

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