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Trigonometric Functions

Multiple Choice Questions

11.

$What is the value of \tan (75 °) + \cot (75 °)$

2
4
$2 \sqrt{3}$
$4 \sqrt{3}$

12.

What is the value of $\cos (46 °) \cos (47 °) \cos (48 °) \cos (49 °) \cos (50 °) . . . \cos (135 °) = ?$

- 1
0
1
Greater than 1

13.
$If \sin (2 θ) = \cos (3 θ), where 0 < θ < \frac{π}{2}, then what is \sin (θ) = ?$

$\frac{\sqrt{5} + 1}{4}$

$\frac{\sqrt{5} - 1}{4}$

$\frac{\sqrt{5} + 1}{16}$

$\frac{\sqrt{5} - 1}{16}$

$\frac{\sqrt{5} - 1}{4}$

$We have, \sin (2 θ) = \cos (3 θ) \sin (2 θ) = \cos (θ + 2 θ) \sin (2 θ) = \cos (θ) \cos (2 θ) - \sin (θ) \sin (2 θ) 2 \sin (θ) \cos (θ) = \cos (θ) (1 - 2 \sin^{2} (θ)) - 2 \sin^{2} (θ) \cos (θ) 2 \sin (θ) = 1 - 2 \sin^{2} (θ) - 2 \sin^{2} (θ) 4 \sin^{2} (θ) + 2 \sin (θ) - 1 = 0 \sin (θ) = \frac{- 2 \pm \sqrt{{(2)}^{2} - 4 (4) (- 1)}}{2 \times 4} \sin (θ) = \frac{- 2 \pm \sqrt{4 + 16}}{8} \sin (θ) = \frac{- 1 \pm \sqrt{5}}{4} \sin (θ) = \frac{\sqrt{5} - 1}{4}$

$0 < θ < \frac{π}{2}$

14.

If the roots of the equation x² + px + q = 0 are tan(19⁰) and tan(26°), then which one of the following is correct?

q - p = 1
p - q = 1
p + q = 2
p + q = 3

15.

what is ${(1 + \tan (α) \tan (β))}^{2} + {(\tan (α) - \tan (β))}^{2} - \sec^{2} (α) \sec^{2} (β) = ?$

16.

If $p = \csc (θ) - \cot (θ) and q = {(\csc (θ) - \cot (θ))}^{- 1}$ , then which one of the following is correct?

pq = 1
p = q
p + q = 1
p + q = 0

17.

What is the least value of 25cosec²(x) + 36sec²(x) ?

18.

$If \sin (θ) + \cos (θ) = \sqrt{2} \cos (θ), then what is (\cos (θ) - \sin (θ)) = ?$

$- \sqrt{2} \cos (θ)$
$- \sqrt{2} \sin (θ)$
$\sqrt{2} \sin (θ)$
$2 \sin (θ)$

19.

$If \sin (θ) = - \frac{1}{2} and \tan (θ) = \frac{1}{\sqrt{3}}, Then in which quadrant does θ lie ?$

First
Second
Third
Fourth

20.

$If \sin (x) = \frac{1}{\sqrt{5}}, \sin (y) = \frac{1}{\sqrt{10}}, where 0 < x < \frac{π}{2}, 0 < y < \frac{π}{2}, then what is (x + y) = ?$

$π$
$\frac{π}{2}$
$\frac{π}{4}$
0

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

13. If sin2θ = cos3θ, where 0 < θ < π2, then what is sinθ = ? 5 + 14 5 - 14 5 + 116 5 - 116

13.
$If \sin (2 θ) = \cos (3 θ), where 0 < θ < \frac{π}{2}, then what is \sin (θ) = ?$

$\frac{\sqrt{5} + 1}{4}$

$\frac{\sqrt{5} - 1}{4}$

$\frac{\sqrt{5} + 1}{16}$

$\frac{\sqrt{5} - 1}{16}$