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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2017 · Mathematics · Inverse Trigonometric Functions

The value of ^ -1 ((3)/(5))+ ^ -1 ((1)/(7))is equal to

The value of sin⁡−1(35)+tan⁡−1(17)isequalto\sin ^{-1} \left(\frac{3}{5}\right)+\tan ^{-1} \left(\frac{1}{7}\right)is equal to

Options

  1. A00
  2. Bπ4\frac{\pi}{4}
  3. Cπ3\frac{\pi}{3}
  4. Dπ2\frac{\pi}{2}

Correct answer

B. π4\frac{\pi}{4}

Step-by-step solution

sin⁡−1(35)+tan⁡−1(17)<br/>\sin ^{-1} \left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right) <br/>\sin θ=35\theta=\frac{3}{5}tan⁡θ=34=tan⁡−1(34)+tan⁡−1(17)\begin{aligned}& \tan \theta=\frac{3}{4}\\ & =\tan ^{-1}\left(\frac{3}{4}\right)+\tan ^{-1}\left(\frac{1}{7}\right)\end{aligned}=\tan ^{-1}\left(\frac{\frac{3}{4}+\frac{1}{7}}{1-\frac{3}{4} \cdot \frac{1}{7}}\right)=\tan ^{-1}\left(\frac{\frac{21+4}{28}}{\frac{28-3}{28}}\right)=\tan ^{-1}\left(\frac{25}{25}\right)=\tan ^^{-1}(1)=\frac{\pi}{4}
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