Trigonometric Ratios Of Compound Angles - Rajasthan Board (RBSE) STD 11 Science MATHS Questions

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

The value of $\frac{\sin5\alpha-\sin\beta}{\cos5\alpha+2\cos4\alpha+\cos3\alpha}$ is:

$\cot\frac{\alpha}{2}$
$\cot\alpha$
$\tan\frac{\alpha}{2}$
None of these

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

The value of $\tan\text{x}+\tan\Big(\frac{\pi}{3}+\text{x}\Big)+\tan\Big(\frac{2\pi}{3}+\text{x}\Big)$ is:

$3\tan3\text{x}$
$\tan3\text{x}$
$3\cot3\text{x}$
$\cot3\text{x}$

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

If $\tan\text{X}=\frac{\text{a}}{\text{b}},$ then $\text{b}\cos2\text{x}+\text{a}\sin2\text{x}$ is equal to:

$\text{a}$
$\text{b}$
$\frac{\text{a}}{\text{b}}$
$\frac{\text{b}}{\text{a}}$

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

The value of $\sin^2\Big(\frac{\pi}{18}\Big)+\sin^2\Big(\frac{\pi}{9}\Big)+\sin^2\Big(\frac{7\pi}{18}\Big)+\sin^2\Big(\frac{4\pi}{9}\Big)$ is:

1
2
3
None of these

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

If $\cos2\text{x}+2\cos\text{x}=1$ then, $(2-\cos^2\text{x})\sin^2\text{x}$ is equal to:

$1$
$-1$
$-\sqrt{5}$
$\sqrt{5}$

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Q 61 Marks Question1 Mark

If $\pi<\text{x}<\frac{3\pi}{2},$ then write the value of $\sqrt{\frac{1-\cos2\text{x}}{1+\cos2\text{x}}}$

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Q 71 Marks Question1 Mark

Prove that:
$\frac{\sin2\text{x}}{1-\cos2\text{x}}=\cot\text{x}$

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Q 81 Marks Question1 Mark

Write the angled triangle ABC, write value of $\sin^2\text{A}\sin^2\text{B}+\sin^2\text{C}.$

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Q 91 Marks Question1 Mark

If $\frac{\pi}{2}<\text{x}<\pi,$ then wrire the value of $\sqrt{\frac{1-\cos^2\text{x}}{1+cos^2\text{x}}}.$

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Q 101 Marks Question1 Mark

If $\tan\text{A}=\frac{1-\cos\text{B}}{\sin\text{B}},$ then find value of $\tan2\text{A}.$

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Q 112 Marks Questions2 Marks

If $\cos\text{x}=\frac{4}{5}$ and x is acute, find $\tan 2\text{x}$

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Q 122 Marks Questions2 Marks

Prove that:
$\frac{\cos2\text{x}}{1+\sin2\text{x}}=\tan(\frac{\pi}{4}-\text{x})$

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Q 132 Marks Questions2 Marks

Prove that:
$\cos^2\frac{\pi}{8}+\cos^2\frac{3\pi}{8}+\cos^2\frac{5\pi}{8}+\cos^2\frac{7\pi}{8}=2$

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Q 142 Marks Questions2 Marks

If $\text{a}\cos2\text{x}+\text{b}\sin2\text{x}=\text{c}$ has $\alpha$ and $\beta$ as its roots, then prove that,
$\tan(\alpha+\beta)=\frac{\text{b}}{\text{a}}$

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Q 152 Marks Questions2 Marks

Prove that:
$1+\cos^22\text{x}=2(\cos^4\text{x}+\sin^4\text{x})$

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Q 163 Marks Question3 Marks

prove that:
$\cos^6\text{x}=\cos2\text{x}=\cos2\text{x}(1-\frac{1}{4}\sin^22\text{x})$

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Q 173 Marks Question3 Marks

Prove that:
$\cot^2\text{x}-\tan^2\text{x}=4\cot2\text{x}\ \text{cosec}\ 2\text{x}$

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Q 183 Marks Question3 Marks

If $\tan\text{x}=\frac{\text{b}}{\text{a}},$ then find the value of $\sqrt{\frac{\text{a+b}}{\text{a}-\text{b}}}+\sqrt{\frac{\text{a}-\text{b}}{\text{a}+\text{b}}}$

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Q 193 Marks Question3 Marks

Prove that:
$\big(\cos\alpha+\cos\beta^2\big)+\big(\sin\alpha+\sin\beta\big)^2=2\cos^2\Big(\frac{\alpha-\beta}{2}\Big)$

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Q 203 Marks Question3 Marks

Prove that:
$\sin4\text{x}=4\sin\text{x}\cos^3\text{x}-4\cos\text{x}\sin^3\text{x}$

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Q 215 Marks Questions5 Marks

Prove that
$\cos\frac{\pi}{65}\cos\frac{2\pi}{65}\cos\frac{4\pi}{65}\cos\frac{8\pi}{65}\cos\frac{16\pi}{65}\cos\frac{32\pi}{65}=\frac{1}{64}$

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Q 225 Marks Questions5 Marks

If $2\tan\alpha=3\tan\beta,$ prove that $\tan(\alpha-\beta)=\frac{\sin2\beta}{5-\cos2\beta}$

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Q 235 Marks Questions5 Marks

$\sin5\text{x}=5\cos^4\text{x}\sin\text{x}-10\cos^2\text{x}\sin^3\text{x}+\sin^5\text{x}$

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Q 245 Marks Questions5 Marks

Prove that:
$\sin6\circ\sin42^\circ\sin66^\circ\sin78^\circ=\frac{1}{16}$

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Q 255 Marks Questions5 Marks

If $\text{a}\cos2\text{x}+\text{b}\sin2\text{x}=\text{c}$ has $\alpha$ and $\beta$ as its roots, then prove that,
$\tan\alpha+\tan\beta=\frac{2\text{b}}{\text{a+c}}$

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Trigonometric Ratios Of Compound Angles question types

Trigonometric Ratios Of Compound Angles questions

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Trigonometric Ratios Of Compound Angles MATHS - Trigonometric Ratios Of Compound Angles

Trigonometric Ratios Of Compound Angles question types

Trigonometric Ratios Of Compound Angles questions

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