Introduction of Trigonometry and its Application - Jharkhand Board (JAC) STD 10 Maths Questions

Q 1M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options.
The value of $(\tan1^\circ\tan2^\circ\tan3^\circ...\tan89^\circ)$ is:

A
0
✓
1
C
2
D
$\frac{1}{2}$

Answer: B.

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Q 2M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options.
If $\sin\text{A}=\frac{1}{2},$ then the value of $\cot\text{A}$ is:

✓
$\sqrt{3}$
B
$\frac{1}{\sqrt{3}}$
C
$\frac{\sqrt{3}}{2}$
D
$1$

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options.
Given that $\sin\alpha=\frac{1}{2}\text{ and }\cos\beta=\frac{1}{2}$ then the value of $(\alpha+\beta)$ is:

A
0º
B
30º
C
60º
✓
90º

Answer: D.

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Q 4M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options. If $4\tan\theta=3,\text{then}\Big(\frac{4\sin\theta-\cos\theta}{4\sin\theta+\cos\theta}\Big)$ is equal to:

A
$\frac{2}{3}$
B
$\frac{1}{3}$
✓
$\frac{1}{2}$
D
$\frac{3}{4}$

Answer: C.

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Q 5M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options.
$\sin(45^\circ+\theta)-\cos(45^\circ-\theta)$ is equal to:

A
$2\cos\theta$
✓
$0$
C
$2\sin\theta$
D
$1$

Answer: B.

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Q 6True False[1 Marks ]1 Mark

Write ‘True’ or ‘False’ and justify your answer.
$\frac{\tan47^\circ}{\cot43^\circ}=1$

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Q 7True False[1 Marks ]1 Mark

Write ‘True’ or ‘False’ and justify your answer.
If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

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Q 8True False[1 Marks ]1 Mark

Write ‘True’ or ‘False’ and justify your answer.
The value of the expression (sin80º - cos80º) is negative.

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Q 9True False[1 Marks ]1 Mark

Write ‘True’ or ‘False’ and justify your answer.
The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.

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Q 10True False[1 Marks ]1 Mark

Write ‘True’ or ‘False’ and justify your answer.
The value of $2\sin\theta\text{can be}\Big(\text{a}+\frac{1}{\text{a}}\Big),$ where a is a positive number, and $\text{a}\neq1.$

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Q 112 Marks Questions2 Marks

Prove the following.
Show that $\tan^4\theta+\tan^2\theta=\sec^4\theta-\sec^2\theta.$

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Q 123 Marks Question3 Marks

Prove the following.
Find the angle of elevation of the sun when the shadow of a pole h metres high is $\sqrt{3}\text{h}$ metres long.

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Q 133 Marks Question3 Marks

Prove the following.
$(\sqrt{3}+1)(3-\cot30^\circ)=\tan^360^\circ-2\sin60^\circ$

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Q 143 Marks Question3 Marks

Prove the following.Simplify $(1+\tan^2\theta)(1-\sin\theta)(1+\sin\theta)$

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Q 153 Marks Question3 Marks

Prove the following.
If $\tan\text{A}=\frac{3}{4},$ then $\sin\text{A}\cos\text{A}=\frac{12}{25}$

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Q 163 Marks Question3 Marks

Prove the following.
A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.

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Q 175 Marks Questions5 Marks

The angle of elevation of the top of a vertical tower from a point on the ground is 60º. From another point 10m vertically above the first, its angle of elevation is 45º. Find the height of the tower.

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Q 185 Marks Questions5 Marks

If $\text{a}\sin\theta+\text{b}\cos\theta=\text{c},$ then prove that $\text{a}\cos\theta-\text{b}\sin\theta=\sqrt{\text{a}^2+\text{b}^2-\text{c}^2}.$

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Q 195 Marks Questions5 Marks

If $\sin\theta+\cos\theta=\text{p and }\sec\theta+\text{cosec}\theta=\text{q},$ then prove that $\text{q}(\text{p}^2-1)=2\text{p}.$

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Q 205 Marks Questions5 Marks

The lower window of a house is at a height of 2m above the ground and its upper window is 4m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be $60^\circ$ and $30^\circ$, respectively. Find the height of the balloon above the ground.

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Q 215 Marks Questions5 Marks

Prove that $\sqrt{\sec^2\theta+\text{cosec}^2\theta}=\tan\theta+\cot\theta.$

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Introduction of Trigonometry and its Application question types

Introduction of Trigonometry and its Application questions

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Introduction of Trigonometry and its Application Maths - Introduction of Trigonometry and its Application

Introduction of Trigonometry and its Application question types

Introduction of Trigonometry and its Application questions

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