Question
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(cos−151) is/are
A
35
B
53
C
−35
D
−53
Answer
53
Explanation
Solution
tan(sec–1x) = sin cos–1(51)
from the given equation it is clear that x is positive.
Let sec–1x = q ̃ secq = x ̃ tanq = 52
̃ x2 = 1 + 54 ̃ x2 = 59 ̃ x = 53