Trigonometric Ratios of Some Particular Angles - Maharashtra Board STD 10 Maths Questions

Q 12 Marks Questions2 Marks

Evaluate the following:
If A = 45°, verify that:
$\cos2\text{A}=2\cos^2\text{A}-1=1-2\sin^2\text{A}$

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Q 22 Marks Questions2 Marks

Evaluate the following:
Verify the following:
$\cos60^\circ\cos30^\circ+\sin60^\circ\sin30^\circ=\cos30^\circ$

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Q 32 Marks Questions2 Marks

Evaluate the following:
$\frac{4}{\cot^230^\circ}+\frac{1}{\sin^230^\circ}-2\cos^245^\circ-\sin^20^\circ$

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Q 42 Marks Questions2 Marks

Evaluate the following:
$\frac{5\cos^260^\circ+4\sec^230^\circ-\tan^245^\circ}{\sin^230^\circ+\cos^230^\circ}$

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Q 52 Marks Questions2 Marks

Evaluate the following:
Show that:
$\frac{\cos30^\circ+\sin60^\circ}{1+\sin30^\circ+\cos60^\circ}=\cos30^\circ$

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Q 63 Marks Question3 Marks

Evaluate the following:
If A and B are acute angle such that $\tan\text{A}=\frac13,\tan\text{B}=\frac12$ and $\tan(\text{A}+\text{B})=\frac{\tan\text{A}+\tan\text{B}}{1-\tan\text{A}\tan\text{B}},$ show that $\text{A}+\text{B}=45^\circ.$

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Q 73 Marks Question3 Marks

Evaluate the following:
Verify the following:
$2\sin45^\circ\cos45^\circ=\sin90^\circ$

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Q 83 Marks Question3 Marks

Evaluate the following:
If A = 30°, verify that:
$\sin2\text{A}=\frac{2\tan\text{A}}{1+\tan^2\text{A}}$

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Q 93 Marks Question3 Marks

Evaluate the following:
If A = 60° and B = 30°, verify that:
$\cos(\text{A}-\text{B})=\cos\text{A}\cos\text{B}+\sin\text{A}\sin\text{B}$

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Q 103 Marks Question3 Marks

Evaluate the following:
If A = 30°, verify that:
$\tan2\text{A}=\frac{2\tan\text{A}}{1-\tan^2\text{A}}$

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Q 114 Marks Questions4 Marks

Evaluate the following:
If A = 60° and B = 30°, verify that:
$\sin(\text{A}-\text{B})=\sin\text{A}\cos\text{B}-\cos\text{A}\sin\text{B}$

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Q 124 Marks Questions4 Marks

Evaluate the following:
If $\sin(\text{A}+\text{B})=1$ and $\cos(\text{A}-\text{B})=1,0^\circ\leq(\text{A}+\text{B})\leq90^\circ$ and $\text{A}>\text{B}$ then find A and B.

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Q 134 Marks Questions4 Marks

Evaluate the following:
If A = 60° and B = 30°, verify that:
$\cos(\text{A}+\text{B})=\cos\text{A}\cos\text{B}-\sin\text{A}\sin\text{B}$

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Q 144 Marks Questions4 Marks

Evaluate the following:
If $\sin(\text{A}+\text{B})=\sin\text{A}\cos\text{B}+\cos\text{A}\sin\text{B}$ and $\cos(\text{A}-\text{B})=\cos\text{A}\cos\text{B}+\sin\text{A}\sin\text{B},$ Find the values of:

$\sin75^\circ$
$\cos15^\circ.$

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Q 154 Marks Questions4 Marks

Evaluate the following:
Using the formula, $\tan2\text{A}=\frac{2\tan\text{A}}{1-\tan^2\text{A}},$ Find the value of $\tan60^\circ,$ it being given that $\tan30^\circ=\frac{1}{\sqrt{3}}.$

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Q 161 Marks Question1 Mark

Evaluate the following:
$\big(\sin^230^\circ+4\cot^230-\frac34\sec^260^\circ\big)\big(\text{cosec}^245^\circ\sec^230^\circ\big)$

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Q 171 Marks Question1 Mark

Evaluate the following:
Show that:
$\frac{1-\sin60^\circ}{\cos60^\circ}=\frac{\tan60^\circ-1}{\tan60^\circ+1}$

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Q 181 Marks Question1 Mark

Evaluate the following:
$\sin60^\circ\cos30^\circ+\cos60^\circ\sin30^\circ$

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Q 191 Marks Question1 Mark

Evaluate the following:
$\cos60^\circ\cos30^\circ+\sin60^\circ\sin30^\circ$