ExamBro
ExamBro
TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(a \tan \alpha+b \tan \beta=(a+b) \tan \left(\frac{\alpha+\beta}{2}\right)\) and \(\alpha-\beta \neq 2 n \pi\) then \(\frac{\cos \beta}{\cos \alpha}=\)

  1. A \(\frac{a}{b}\)
  2. B \(\frac{a+b}{a-b}\)
  3. C \(\frac{a^2-b^2}{a^2+b^2}\)
  4. D \(\frac{b}{a}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{b}{a}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {} \mathrm{a} \tan \alpha+\mathrm{b} \tan \beta=\mathrm{a} \tan \left(\frac{\alpha+\beta}{2}\right)+\mathrm{b} \tan \left(\frac{\alpha+\beta}{2}\right) \\ & \mathrm{a}\left(\tan \alpha-\tan \frac{\alpha+\beta}{2}\right)=\mathrm{b}\left(\tan…