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If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x. - Mathematics and Statistics

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प्रश्न

If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.

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उत्तर

As we know that

 2 tan–1(x) = `tan^-1 ((2x)/(1 - x^2))`

∴ 2 tan–1(cos x) = `tan^-1 ((2 cos x)/(1 - cos^2x))`

⇒ 2 tan–1(cos x) = `tan^-1 ((2 cos x)/(sin^2x))`

Given, 2 tan–1 (cos x) = tan–1 (2 cosec x)

∴ `tan^-1 ((2 cos x)/(sin^2x))` = tan–1 (2 cosec x)  ......[From (i)]

⇒ `(2 cos x)/sin^2x `= 2 cosec x

⇒ `cosx/sin^2x = 1/sinx`

⇒ cos x = sin x

⇒ x = `π/4`

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Trigonometric Equations and Their Solutions
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2021-2022 (March) Set 1

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