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Question: The values of x satisfying tan(sec<sup>–1</sup>x) = \(\sin(\cos^{- 1}\frac{1}{\sqrt{5}})\) is/are...

The values of x satisfying tan(sec–1x) = sin(cos115)\sin(\cos^{- 1}\frac{1}{\sqrt{5}}) is/are

A

53\frac{\sqrt{5}}{3}

B

35\frac{3}{\sqrt{5}}

C

53- \frac{\sqrt{5}}{3}

D

35- \frac{3}{\sqrt{5}}

Answer

35\frac{3}{\sqrt{5}}

Explanation

Solution

tan(sec–1x) = sin cos–1(15)\left( \frac{1}{\sqrt{5}} \right)

from the given equation it is clear that x is positive.

Let sec–1x = q ̃ secq = x ̃ tanq = 25\frac{2}{\sqrt{5}}

̃ x2 = 1 + 45\frac{4}{5} ̃ x2 = 95\frac{9}{5} ̃ x = 35\frac{3}{\sqrt{5}}