Trigonometry (Basic)

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

Click on each question to see answer & solution.

Question No: #91

Prove that, `\frac{1 + cos A - sin A}{1 + cos A + sin A} = \frac{cos A}{1 + sin A}`.

Question No: #92

If the angles `A` and `B` are complimentary to each other, then value of-
(i) `sin (A+B)` is ........
(ii) `\frac{1}{\text{cosec}^2 A} + \frac{1}{\text{cosec}^2 B} + \frac{1}{sin^2 (A+B)} = ` .......
(iii) `(1 - sin^2 A)(1 - cos^2 A)(1 + cot^2 B)(1 + tan^2 B) = ` ...... .
Ans: (i) `1`, (ii) `2`, (iii) `1`
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Question No: #93

Find the complimentary angle of 63°35'15"
Ans: 26°24′45′′
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Question No: #94

Circular value of angle supplementary to 75° angle is -
(a) `\frac{\pi}{2}^c`, (b) `\frac{3\pi}{12}^c`, (c) `\frac{5\pi}{12}^c`, (d) `\frac{7\pi}{12}^c`
Ans: (d) `\frac{7\pi}{12}^c`
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Question No: #95

Circular value of the angle complimentary to `x°` is .........
Ans: `\pi/2 (1 - x/90)^c`
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Question No: #96

Circular value of the angle complementary to `22.5^\circ` is -
(a) `\frac{3\pi}{8}`, (b) `\frac{\pi}{4}`, (c) `\frac{\pi}{8}`, (d) `\frac{3\pi}{4}`
Ans: (a) `\frac{3\pi}{8}`
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Question No: #97

If `tan 22\frac{1}{2}^\circ = \sqrt{2}-1`, then the value of `cot 67\frac{1}{2}^\circ` is -
(a) `\sqrt{2}+1`, (b) `\sqrt{2}-1`, (c) `\sqrt{3}-1`, (d) `\frac{\sqrt{3}-1}{\sqrt{2}+1}`
Ans: (b) `\sqrt{2}-1`
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Question No: #98

If `cos 27^\circ = x`, then the value of `tan 63^\circ` is -
(a) `\frac{\sqrt{1-x^2}}{x}`, (b) `\frac{x}{\sqrt{1-x^2}}`, (c) `\frac{x}{\sqrt{1+x^2}}`, (d) `\frac{x}{\sqrt{x^2-1}}`
Ans: (b) `\frac{x}{\sqrt{1-x^2}}`
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Question No: #99

Value of `tan 15° tan 45° tan 60° tan 75°` is -
(a) `\frac{1}{\sqrt{3}}`, (b) `1`, (c) `\sqrt{3}`, (d) undefined
Ans: (c) `\sqrt{3}`
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Question No: #100

Value of `sin 43^\circ cos47^\circ + cos43^\circ sin 47^\circ` is -
(a) `0`, (b) `1`, (c) `1/\sqrt{2}`, (d) `\sqrt{3}/2`
Ans: (b) `1`
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