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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
$\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{3}{5}=$
  • ✓
    $\tan ^{-1} \frac{27}{11}$
  • B
    $\sin ^{-1} \frac{11}{27}$
  • C
    $\cos ^{-1} \frac{11}{27}$
  • D
    $\cot ^{-1} \frac{27}{11}$
✓

Answer

Correct option: A.
$\tan ^{-1} \frac{27}{11}$
(A) Let $\alpha=\cos ^{-1}\left(\frac{4}{5}\right)$
$\therefore \cos \alpha=\left(\frac{4}{5}\right) \Rightarrow \tan \alpha=\left(\frac{3}{4}\right)$
$\therefore \quad \alpha=\tan ^{-1}\left(\frac{3}{4}\right)$
$\therefore \quad \cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{3}{5}=\tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{3}{5}$
$=\tan ^{-1}\left(\frac{\frac{3}{4}+\frac{3}{5}}{1-\frac{3}{4} \cdot \frac{3}{5}}\right)=\tan ^{-1}\left(\frac{27}{11}\right)$

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