Transformation Formulae - Rajasthan Board (RBSE) STD 11 Science MATHS Questions

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

$\text{If}\ \sin\alpha+\sin\beta=\text{a}\text{ and }\cos\alpha-\cos\beta=\text{b},\ \text{than }\tan\frac{\alpha-\beta}{2}=$

$-\frac{\text{a}}{\text{b}}$
$-\frac{\text{b}}{\text{a}}$
$\sqrt{\text{a}^2+\text{b}^2}$
None of these

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

The value of $\cos52^\circ+\cos68^\circ+\cos172^\circ\text{ is }$

$0$
$1$
$2$
$\frac{3}{2}$

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

The value of $\sin78^\circ-\sin66^\circ-\sin42^\circ+\sin6^\circ\text{ is }$

$\frac{1}{2}$
$-\frac{1}{2}$
$-1$
None of these

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

If $\tan\alpha=\frac{\text{x}}{\text{x}+1}\text{ and }\tan\beta=\frac{1}{2\text{x}+1},$ than $\alpha+\beta$ is equal to

$\frac{\pi}{2}$
$\frac{\pi}{3}$
$\frac{\pi}{6}$
$\frac{\pi}{4}$

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

If $\sin\text{x}+\sin\text{y}=\sqrt3(\cos\text{y}-\cos\text{x}),$ than $\sin3\text{x}+\sin3\text{y}=$

$2\sin3\text{x}$
$0$
$1$
None of these

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Q 61 Marks Question1 Mark

Express the following as the sum or difference of sines and cosines:
$2\sin3\text{x}\cos\text{x}$

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Q 71 Marks Question1 Mark

If $\sin\text{A}+\sin\text{B}=\alpha\text{ and }\cos\text{A}+\cos\text{B}=\beta,$
than write the value of $\tan\Big(\frac{\text{A+B}}{2}\Big).$

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Q 81 Marks Question1 Mark

Write the value of $\frac{\sin\text{A}+\sin3\text{A}}{\cos\text{A}+\cos3\text{A}}.$

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Q 91 Marks Question1 Mark

Prove that:
$2\cos\frac{5\pi}{12}\cos\frac{\pi}{12}=\frac{1}{2}$

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Q 101 Marks Question1 Mark

If $(\cos\alpha+\cos\beta)^2+(\sin\alpha+\sin\beta)^2=\lambda\cos^2\Big(\frac{\alpha-\beta}{2}\Big),$ write the value of $\lambda.$

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Q 112 Marks Questions2 Marks

Prove that:
$\sin65^\circ+\cos65^\circ=\sqrt2\cos20^\circ$

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Q 122 Marks Questions2 Marks

Prove that:
$\sin80^\circ-\cos70^\circ=\cos50^\circ$

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Q 132 Marks Questions2 Marks

Prove that:
$\sin47^\circ+\cos77^\circ=\cos17^\circ$

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Q 142 Marks Questions2 Marks

Prove that:
$\sin\frac{5\pi}{18}-\cos\frac{4\pi}{9}=\sqrt3\sin\frac{\pi}{9}$

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Q 152 Marks Questions2 Marks

Prove that:
$\sin105^\circ+\cos105^\circ=\cos45^\circ$

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Q 163 Marks Question3 Marks

Prove that:
$\frac{\sin9\text{A}-\sin\text7{A}}{\cos7\text{A}-\cos9\text{A}}=\cot8\text{A}$

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Q 173 Marks Question3 Marks

$\text{If}\ \text{cosec}\text{A}+\sec\text{A}=\text{cosecB}+\sec\text{B},$ prove that:
$\tan\text{A}\tan\text{B}=\cot\frac{\text{A+B}}{2}$

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Q 183 Marks Question3 Marks

Prove that:
$\frac{\sin\text{A}-\sin\text{B}}{\cos\text{A}+\cos\text{B}}=\tan\frac{\text{A}-\text{B}}{2}$

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Q 195 Marks Questions5 Marks

Prove that:
$\cos20^\circ\cos100^\circ+\cos100^\circ\cos140^\circ-\cos140^\circ\cos200^\circ=-\frac{3}{4}$

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Q 205 Marks Questions5 Marks

Prove that:
$\sin20^\circ\sin40^\circ\sin80^\circ=\frac{\sqrt3}{8}$

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Q 215 Marks Questions5 Marks

Prove that:
$\cos\text{A}+\cos3\text{A}+\cos5\text{A}+\cos7\text{A}=4\cos\text{A}\cos2\text{A}\cos4\text{A}$

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Q 225 Marks Questions5 Marks

Prove that:
$\frac{\sin\text{A}+\sin\text3{A}}{\cos\text{A}-\cos3\text{A}}=\cot\text{A}$

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Q 235 Marks Questions5 Marks

Show that:

$\sin\text{A}\sin(\text{B}-\text{C})+\sin\text{B}\sin(\text{C}-\text{A})+\sin\text{C}\sin(\text{A}-\text{B})=0$

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Transformation Formulae MATHS - Transformation Formulae

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