TS EAMCET · Maths · Inverse Trigonometric Functions
If \(\sin ^{-1}(4 x)-\cos ^{-1}(3 x)=\frac{\text { g }}{6}\), then \(x=\)
- A \(\frac{\sqrt{3}}{2 \sqrt{7}}\)
- B \(\frac{\sqrt{3}}{4 \sqrt{7}}\)
- C \(\frac{\sqrt{3}}{2 \sqrt{13}}\)
- D \(\frac{\sqrt{3}}{4 \sqrt{13}}\)
Answer & Solution
Correct Answer
(C) \(\frac{\sqrt{3}}{2 \sqrt{13}}\)
Step-by-step Solution
Detailed explanation
\(\sin ^{-1}(4 x)-\cos ^{-1}(3 x)=\frac{\pi}{6}\)....(i) Let, \(A=\sin ^{-1}(4 x), B=\cos ^{-1}(3 x)\) \(\sin A=4 x \Rightarrow \cos A=\sqrt{1-16 x^2}\) \(\cos B=3 x \Rightarrow \sin B=\sqrt{1-9 x^2}\) \(A-B=\frac{\pi}{6} \Rightarrow \sin (A-B)=\frac{1}{2} \quad[\) From (i)]…
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