MHT CET · Maths · Trigonometric Equations
If \(\sec x+\tan x=2, \quad 0 < x < \frac{\pi}{2}\) then \(\sin \frac{x}{4}\)
- A \(\frac{1}{\sqrt{10+3 \sqrt{10}}}\)
- B \(\frac{1}{\sqrt{2(10+3 \sqrt{10})}}\)
- C \(\frac{1}{\sqrt{10-3 \sqrt{10}}}\)
- D \(\frac{1}{2 \sqrt{10-3 \sqrt{10}}}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\sqrt{2(10+3 \sqrt{10})}}\)
Step-by-step Solution
Detailed explanation
\(\sec x - \tan x = \frac{1}{\sec x + \tan x} = \frac{1}{2}\) \(2\sec x = 2 + \frac{1}{2} = \frac{5}{2} \Rightarrow \cos x = \frac{4}{5}\)
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