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← JEE Advanced 2015 · Paper 2
MathematicsMultiple correct+4 / -2Question 50 of 60

JEE Advanced 2015 · Paper 2, Mathematics question 50

If α=3sin⁡−1(611)\alpha=3\sin^{-1}\left(\dfrac6{11}\right) and β=3cos⁡−1(49)\beta=3\cos^{-1}\left(\dfrac49\right), where the inverse trigonometric functions take only the principal values, then the correct option(s) is(are)

Choose one or more options
Answer and worked solution

Official answer: B, C, D

Locate α. 611>12\frac6{11}>\frac12, so sin⁡−1611≈0.577\sin^{-1}\frac6{11}\approx0.577 rad and α≈1.73\alpha\approx1.73 rad (≈99°). So cos⁡α<0\cos\alpha<0. (D) is true.

Locate β. cos⁡−149≈1.110\cos^{-1}\frac49\approx1.110 rad, so β≈3.33\beta\approx3.33 rad (≈191°), in the third quadrant.

  • sin⁡β<0\sin\beta<0: (B) is true.
  • cos⁡β<0\cos\beta<0: (A) is false.

Locate α + β. α+β≈5.06\alpha+\beta\approx5.06 rad (≈290°), in the fourth quadrant, so cos⁡(α+β)>0\cos(\alpha+\beta)>0. (C) is true.

(B), (C), (D)

Topics:Inverse trigonometric functions
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