AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\cos x+\sin x=\frac{1}{2}\) and \(0 < x < \pi\), then \(\tan x=\)
- A \(\frac{1+\sqrt{7}}{4}\)
- B \(\frac{1-\sqrt{7}}{4}\)
- C \(\frac{4-\sqrt{7}}{3}\)
- D \(-\frac{(4+\sqrt{7})}{3}\)
Answer & Solution
Correct Answer
(D) \(-\frac{(4+\sqrt{7})}{3}\)
Step-by-step Solution
Detailed explanation
\( \cos x+\sin x=\frac{1}{2} \) \( (\cos x+\sin x)^2 = (\frac{1}{2})^2 \) \( 1 + 2\sin x \cos x = \frac{1}{4} \) \( 2\sin x \cos x = -\frac{3}{4} \) Given \( 0 0 \) and \( \cos x Therefore, \( x \) is in Quadrant II, which means \( \tan x Let \( t = \tan x \). In Quadrant II,…
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