Trigonometry (Basic)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #31

If `sin (\theta + 30^\circ) = 1`, then the value of `cot \frac{\theta}{2}` is ........
Ans: `\sqrt{3}`
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Question No: #32

If `2 cos 3\theta = 1`, then value of `\theta` is -
(a) 10°, (b) 15°, (c) 20°, (d) 30°
Ans: (c) 20°
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Question No: #33

If `sin \theta = cos \theta`, then value of `2\theta` is -
(a) 90°, (b) 60°, (c) 45°, (d) 30°
Ans: (a) 90°
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Question No: #34

If `sin \theta - cos \theta = 0`, (`0^\circ \le \theta \le 90^\circ`) and `sec \theta + \text{cosec}\ \theta = x`, then the value of `x` is -
(a) `1`, (b) `2`, (c) `\sqrt{2}`, (d) `2\sqrt{2}`
Ans: (d) `2\sqrt{2}`
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Question No: #35

If `tan \theta = cot \theta` and `\theta` be an acute angle, then find the value of `tan(\theta + 15^\circ)` .
Ans: `\sqrt{3}`
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Question No: #36

If `cot \theta = tan (n-1)\theta`, then value of `\theta` is -
(a) `{2\pi}/\n`, (b) `\pi/n`, (iii) `{(n-1)\pi}/2`, (d) `\pi/{2n}`
Ans: (d) `\pi/{2n}`
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Question No: #37

For which values of `\theta (0^\circ \le \theta \le 90^\circ)`, the equation `2 sin \theta cos \theta = cos \theta` will be valid?
Ans: `30^\circ, 90^\circ`
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Question No: #38

Find the values of `\theta` from the equation `2 cos^2 \theta - 3 cos \theta + 1 = 0` where `0^\circ \le \theta \le 90^\circ`.
Ans: `0^\circ, 60^\circ`
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Question No: #39

Find the value of `theta`, that satisfies the equation `3 - 3 sin\theta - cos^2 \theta=0`, where `0^\circ \le \theta \le 90^\circ`
Ans: `90^\circ`
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Question No: #40

If `3x = \text{cosec} \quad \alpha` and `3/x = cot \alpha`, then the value of `3(x^2 - 1/x^2)` is -
(a) `1/27`, (b) `1/81`, (c) `1/3`, (d) `1/9`
Ans: (c) `1/3`
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