Trigonometry (Basic)

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

Click on each question to see answer & solution.

Question No: #111

Find the value of `(tan 1^\circ \times tan 2^\circ \times tan 3^\circ \times ... \times tan 89^\circ)`.

Question No: #112

If `A, B, C` are three angles of a right angled triangle, then the value of `sin^2 A + sin^2 B + sin^2 C` is -
(a) 0, (b) 1, (c) 2, (d) 3
Ans: (c) 2
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Question No: #113

In `\triangle ABC`, show that, `sin \frac{A+B}{2} = cos C/2`.

Question No: #114

If `sin^2 A + sin^2 B = 1`, then find the value of `cot (A+B)`.
Ans: `0`
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Question No: #115

If `tan 35^\circ tan 55^\circ = sin \theta`, then find the value of `\theta`.
Ans: `90^\circ`
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Question No: #116

If `tan \frac{\theta}{4} \cdot tan \theta = 1`, then the value of `\theta` is ........
Ans: `72^\circ`
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Question No: #117

If `tan \theta \cdot tan \phi = 1`, then the value of `sin (\frac{\theta + \phi}{3})` is -
(a) `1`, (b) `1/sqrt{2}`, (c) `\sqrt{3}/2`, (d) `1/2`
Ans: (d) `1/2`
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Question No: #118

If `tan 4\theta \cdot tan 6\theta = 1`, then the value of `tan 5\theta` is ........

Question No: #119

If `sec 5\theta = \text{cosec}\quad(\theta + 36^\circ)` and `5\theta` acute angle, then find the value of `\theta`.
Ans: `9^\circ`
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Question No: #120

If `sin 10 \theta = cos 8 \theta`, where `0^\circ \lt \theta \lt 90^\circ`, then find the value of `\theta`.
Ans: `5^\circ`
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