TS EAMCET · Maths · Trigonometric Equations
If \(y=\log _e \tan \left(\frac{\pi}{4}+\frac{x}{2}\right)\), then \(\tan h\left(\frac{y}{2}\right)=\)
- A \(\cot \frac{x}{2}\)
- B \(\tan x\)
- C \(\cot h x\)
- D \(\tan \frac{x}{2}\)
Answer & Solution
Correct Answer
(D) \(\tan \frac{x}{2}\)
Step-by-step Solution
Detailed explanation
It is given that \(y=\log _c \tan \left(\frac{\pi}{4}+\frac{x}{2}\right)\) \(\Rightarrow \quad e^y=\frac{1+\tan \frac{x}{2}}{1-\tan \frac{x}{2}}\) \(\tan h\left(\frac{y}{2}\right)=\frac{e^{\frac{y}{2}}-e^{-\frac{y}{2}}}{e^{\frac{y}{2}}+e^{-\frac{y}{2}}}=\frac{e^y-1}{e^y+1}\)…
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