Trigonometric Ratios - Maharashtra Board STD 10 Maths Questions

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

The value of $\frac{\cos^320^\circ-\cos^370^\circ}{\sin^370^\circ-\sin^320^\circ}$ is:

A
$\frac{1}{2}$
B
$\frac{1}{\sqrt{2}}$
✓
$1$
D
$2$

Answer: C.

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

$\tan5^\circ\times\tan30^\circ\times4\tan85^\circ$ is equal to:

✓
$\frac{4}{\sqrt{3}}$
B
$4\sqrt{3}$
C
$1$
D
$4$

Answer: A.

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

The value of $\tan1^\circ\tan2^\circ\tan3^\circ.....\tan89^\circ$ is:

✓
$1$
B
$-1$
C
$0$
D
None of these

Answer: A.

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

If $\text{x}\tan45^\circ\cos60^\circ=\sin60^\circ\cot60^\circ,$ then $x$ is equal to:

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

Answer: A.

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

$\frac{2\tan30^\circ}{1-\tan^230^\circ}$ is equal to:

A
$\cos60^\circ$
B
$\sin60^\circ$
✓
$\tan60^\circ$
D
$\sin30^\circ$

Answer: C.

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Q 62 Marks Questions2 Marks

Evaluate the following:
$\frac{\sec70^\circ}{\text{cosec }20^\circ}+\frac{\sin59^\circ}{\cos31^\circ}$

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Q 72 Marks Questions2 Marks

Express the following in terms of trigonometric ratios of angles lying between 0° and 45°.$\cos78^\circ+\sec78^\circ$

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Q 82 Marks Questions2 Marks

Evaluate the following:
$\text{cosec 31}^\circ-\sec59^\circ$

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Q 92 Marks Questions2 Marks

Find the value of x in the following:
$\cos2\text{x}=\cos60^\circ\cos30^\circ+\sin60^\circ\sin30%\circ$

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Q 102 Marks Questions2 Marks

Evaluate:
$=\frac{\sin50^\circ}{\cos40^\circ}+\frac{\text{cosec }40^\circ}{\sec50^\circ}-4 \cos50^\circ\ \text{cosec }40^\circ$

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Q 113 Marks Question3 Marks

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\tan\theta=11$

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Q 123 Marks Question3 Marks

If $\sec\text{A}=\frac{17}{8},$ verify that $\frac{3-4\sin^2\text{A}}{4\cos^2\text{A}-3}=\frac{3-\tan^2\text{A}}{1-3\tan^2\text{A}}.$

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Q 133 Marks Question3 Marks

Evaluate the following:
$\frac{\tan45^\circ}{\text{cosec}30^\circ}+\frac{\sec60^\circ}{\cot45^\circ}-\frac{5\sin90^\circ}{2\cos0^\circ}$

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Q 143 Marks Question3 Marks

If A = 30° and B = 60°, verify that.
$\sin(\text{A}+\text{B})=\sin\text{A}\cos\text{B}+\cos\text{A}\sin\text{B}$

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Q 153 Marks Question3 Marks

If $\tan\theta=\frac{20}{21},$ show that $\frac{1-\sin\theta+\cos\theta}{1+\sin\theta+\cos\theta}=\frac{3}{7}.$

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Q 164 Marks Questions4 Marks

If $\sec\theta=\frac{5}{4},$ find the value of $\frac{\sin\theta-2\cos\theta}{\tan\theta-\cot\theta}.$

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Q 174 Marks Questions4 Marks

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\sec\theta=\frac{13}{5}$

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Q 184 Marks Questions4 Marks

If $3\cot\theta=2,$ find the value of $\frac{4\sin\theta-3\cos\theta}{2\sin\theta+6\cos\theta}.$

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Q 194 Marks Questions4 Marks

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\cot\theta=\frac{12}{5}$

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Q 204 Marks Questions4 Marks

If $\cos\theta=\frac{3}{5},$ find the value of $\frac{\sin\theta-\frac{1}{\tan\theta}}{2\tan\theta}.$

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Q 211 Marks Question1 Mark

What is the maximum value of $\frac{1}{\sec\theta}?$

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Q 221 Marks Question1 Mark

Write the maximum and minimum values of $\sin\theta.$

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Trigonometric Ratios Maths - Trigonometric Ratios

Trigonometric Ratios question types

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