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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(\cos ^2 84^{\circ}+\sin ^2 126^{\circ}-\sin 84^{\circ} \cos 126^{\circ}=K\) and \(\cot A+\) \(\tan A=2 K\), then the possible values of \(\tan A\) are

  1. A \(\frac{2}{3}, \frac{3}{2}\)
  2. B \(\frac{1}{3}, 3\)
  3. C \(\frac{1}{3}, 3\)
  4. D \(\frac{3}{4}, \frac{4}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{3}, 3\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } \cos ^2 84^{\circ}+\sin ^2 126^{\circ}-\sin 84^{\circ} \cos 126^{\circ}=K \\ & \Rightarrow \frac{1+\cos 168^{\circ}}{2}+\sin ^2(90+36)^{\circ}-\frac{1}{2}\left[\sin 210^{\circ}-\sin 42^{\circ}\right]=K \\ & \Rightarrow \frac{1+\cos…