AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(A\) and \(B\) are the values such that \((A+B)\) and \((A-B)\) are not odd multiples of \(\frac{\pi}{2}\) and \(2 \tan (A+B)=3 \tan (A-B)\), then \(\sin A \cos A=\)
- A \(\sin B \cos B\)
- B \(5 \sin \mathrm{~B} \cos \mathrm{~B}\)
- C \(\sin 2 B\)
- D \(\cos 2 \mathrm{~B}\)
Answer & Solution
Correct Answer
(B) \(5 \sin \mathrm{~B} \cos \mathrm{~B}\)
Step-by-step Solution
Detailed explanation
\(2 \tan (A+B)=3 \tan (A-B)\) \(\frac{\tan (A+B)}{\tan (A-B)}=\frac{3}{2}\) \(\frac{\tan (A+B)+\tan (A-B)}{\tan (A+B)-\tan (A-B)}=\frac{3+2}{3-2}\) \(\frac{\sin (A+B) \cos (A-B)+\cos (A+B) \sin (A-B)}{\sin (A+B) \cos (A-B)-\cos (A+B) \sin (A-B)}=5\)…
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