TS EAMCET · Maths · Trigonometric Equations
If \(\cot \left(\frac{A}{2}\right)=\sqrt{\frac{1+a}{1-a}} \cdot \cot \left(\frac{\theta}{2}\right)\), then \(\cos \theta=\)
- A \(\frac{(\cos A)+a}{1-a \cos A}\)
- B \(\frac{(\cos A)-a}{1-\operatorname{acos} A}\)
- C \(\frac{(\cos A)-a}{1+a \cos A}\)
- D \(\frac{(\cos A)+a}{1+a \cos A}\)
Answer & Solution
Correct Answer
(B) \(\frac{(\cos A)-a}{1-\operatorname{acos} A}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { We have, } \cot \frac{A}{2}=\sqrt{\frac{1+a}{1-a}} \cot \frac{\theta}{2} \\ & \Rightarrow \quad \cot ^2 \frac{A}{2}=\left(\frac{1+a}{1-a}\right) \cot ^2 \frac{\theta}{2}\end{aligned}\)…
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