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AP EAMCET · Maths · Trigonometric Equations

If \(\tan A=\tan \alpha \operatorname{coth} x=\cot \beta \tanh x\), then \(\tan (\alpha+\beta)=\)

  1. A \(\cosh 2 x \operatorname{cosec} 2 A\)
  2. B \(\sinh 2 x \cos 2 \mathrm{~A}\)
  3. C \(\cosh 2 x \sec 2 \mathrm{~A}\)
  4. D \(\sinh 2 x \operatorname{cosec} 2 A\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\sinh 2 x \operatorname{cosec} 2 A\)

Step-by-step Solution

Detailed explanation

Given: \(\tan \mathrm{A}=\tan \alpha \cot h x=\cot \mathrm{B} \tan h x\) ...(i) \(\tan \alpha=\frac{\tan \mathrm{A}}{\cot h x}=\tan \mathrm{A} \cdot \tan h x\) ...(ii) \(\cot \beta=\frac{\tan \mathrm{A}}{\tan h x} \Rightarrow \tan \mathrm{B}=\frac{\tan h x}{\tan \mathrm{A}}\)…