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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2018 · Mathematics · Inverse Trigonometric Functions

Let the slope of the curve y= ^ -1 ( x) be θ : Then the value of θ...

Let the slope of the curve y=cos⁡−1(sin⁡x)y=\cos ^{-1}(\sin x) be tan⁡θ\tan \theta : Then the value of θ\theta in the interval (0,π)(0, \pi) is

Options

  1. Aπ6\frac{\pi}{6}
  2. B3π4\frac{3 \pi}{4}
  3. Cπ4\frac{\pi}{4}
  4. Dπ2\frac{\pi}{2}

Correct answer

B. 3π4\frac{3 \pi}{4}

Step-by-step solution

y=cos⁡−1(sin⁡x)=cos⁡−1cos⁡(π2−x) and  =π2−x\begin{aligned}& y=\cos ^{-1}(\sin x) \\ & =\cos ^{-1} \cos \left(\frac{\pi}{2}-x\right)\\ \text{\text{ and } } =\frac{\pi}{2}-x \end{aligned} From question, slope of the curve m=tan⁡θ∴tan⁡θ=−1⇒θ=3π4m=\tan \theta\therefore \quad \tan \theta=-1 \Rightarrow \theta=\frac{3 \pi}{4}
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