JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Considering the principal values of inverse trigonometric functions, the value of the expression \(\tan\left(2 \sin^{-1}\left(\frac{2}{\sqrt{13}}\right)-2 \cos^{-1}\left(\frac{3}{\sqrt{10}}\right)\right)\) is equal to:
- A \(-\frac{33}{56}\)
- B \(\frac{33}{56}\)
- C \(\frac{16}{63}\)
- D \(-\frac{16}{63}\)
Answer & Solution
Correct Answer
(B) \(\frac{33}{56}\)
Step-by-step Solution
Detailed explanation
Let \(\sin^{-1}\frac{2}{\sqrt{13}}=\theta~\&\cos^{-1}\frac{3}{\sqrt{10}}=\phi\) \(\sin \theta=\frac{2}{\sqrt{13}}~\&\cos \phi=\frac{3}{\sqrt{10}}\) \(\tan(2\theta-2\phi)=\frac{\tan 2\theta-\tan 2\phi}{1+\tan 2\theta \tan 2\phi}\)…
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