Trigonometry (Basic)

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

Click on each question to see answer & solution.

Question No: #71

If `\frac{5 cot \theta + \text{cosec}\ \theta}{5 cot \theta - \text{cosec}\ \theta} = 7/3`, then find the value of `cos \theta`.
Ans: `1/2`
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Question No: #72

If `cot \theta = x/y`, then prove that, `\frac{x cos \theta - y sin \theta}{x cos \theta + y sin \theta} = \frac{x^2 - y^2}{x^2 + y^2}`.

Question No: #73

If `m(\text{cosec}\ \theta + cot \theta) = x` and `n(\text{cosec}\ \theta - cot \theta) = y`, then find the relation between `x` and `y` by eliminating `\theta`.
Ans: `xy = mn`
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Question No: #74

If `tan \theta + sin \theta = m` and `tan \theta - sin \theta = n`, then prove that, `m^2 - n^2 = 4 \sqrt{mn}`.

Question No: #75

If `x = a sec \theta`, `y = b tan \theta`, then prove that `x^2/a^2 - y^2/b^2 = 1`.

Question No: #76

Eliminate `\theta` from the equations `x = a sin \theta` and `y = b tan \theta`.
Ans: `a^2/x^2 - b^2/y^2 = 1`
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Question No: #77

Find the relation between `x` and `y` by eliminating `\theta` from the equations `2x = 3 sin \theta` and `5y = 3 cos \theta`.
Ans: `4x^2 + 25y^2 = 9`
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Question No: #78

Find the relation between `x` and `y` by eliminating `\theta` from the equations `x\ cos \theta = 3` and `4\ tan \theta = y`.
Ans: `x^2/9 - y^2/16 = 1`
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Question No: #79

If `x = a cos \theta + b sin \theta` and `y = a sin \theta - b cos \theta`, then prove that `x^2 + y^2 = a^2 + b^2`.

Question No: #80

For any value of `\theta`, maximum value of `5+4 sin \theta` is -
(a) 9, (b) 1, (c) 0, (d) 5
Ans: (a) 9
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