AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\tan \theta=\frac{\cos 25^{\circ}+\sin 25^{\circ}}{\cos 25^{\circ}-\sin 25^{\circ}}\) and \(\theta\) is in the third quadrant, then \(\theta=\)
- A \(200^{\circ}\)
- B \(205^{\circ}\)
- C \(225^{\circ}\)
- D \(250^{\circ}\)
Answer & Solution
Correct Answer
(D) \(250^{\circ}\)
Step-by-step Solution
Detailed explanation
\[ \begin{gathered} \text { If } \tan \theta=\frac{\cos 25^{\circ}+\sin 25^{\circ}}{\cos 25^{\circ}-\sin 25^{\circ}}=\frac{1+\tan 25^{\circ}}{1-\tan 25^{\circ}} \\ =\tan \left(45^{\circ}+25^{\circ}\right) \end{gathered} \] \(\because \theta\) is in the third quadrant, so…
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