Transformation Formulae - Uttarakhand Board (UBSE) STD 11 Science Maths Questions

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

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

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

Answer: B.

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

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

✓
$0$
B
$1$
C
$2$
D
$\frac{3}{2}$

Answer: A.

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

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

A
$\frac{1}{2}$
✓
$-\frac{1}{2}$
C
$-1$
D
None of these

Answer: B.

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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

A
$\frac{\pi}{2}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{6}$
✓
$\frac{\pi}{4}$

Answer: D.

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

$\sin163^\circ\cos347^\circ+\sin73^\circ\sin167^\circ=$

A
$0$
✓
$\frac{1}{2}$
C
$1$$$
D
None of these

Answer: B.

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Q 61 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 71 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 81 Marks Question1 Mark

If $\text{A}+\text{B}=\frac{\pi}{3}\text{ and }\cos\text{A}+\cos\text{B}=1,$ than find the value of $\cos\frac{\text{A}-\text{B}}{2}.$

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Q 91 Marks Question1 Mark

Express the following as the product of sines and cosines:
$\sin5\text{x}-\sin\text{x}$

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Q 101 Marks Question1 Mark

$\text{If }\cos(\text{A+B})\sin(\text{C}-\text{D})=\cos(\text{A}-\text{B})\sin(\text{C+D}),$
than write the value $\tan\text{A}\tan\text{B}\tan\text{C}.$

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Q 112 Marks Questions2 Marks

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

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Q 122 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 132 Marks Questions2 Marks

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

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Q 142 Marks Questions2 Marks

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

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Q 152 Marks Questions2 Marks

Prove that:
$\cos80^\circ+\cos40^\circ-\cos20^\circ=0$

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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

$\text{If}\ \cos(\text{A+B})\sin(\text{C}-\text{D})=\cos(\text{A}-\text{B})\sin(\text{C+D}),$
prove that $\tan\text{A}\tan\text{B}\tan\text{C}+\tan\text{D}=0$

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Q 205 Marks Questions5 Marks

Prove that:
$\sin\text{A}+\sin2\text{A}+\sin4\text{A}+\sin5\text{A}=4\cos\frac{\text{A}}{2}\cos\frac{2\text{A}}{2}\cos4\text{A}$

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Q 215 Marks Questions5 Marks

Prove that:
$\tan20^\circ\tan40^\circ\tan60^\circ\tan80^\circ=3$

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Q 225 Marks Questions5 Marks

Prove that:
$\sin10^\circ\sin50^\circ\sin60^\circ\sin70^\circ=\frac{\sqrt3}{16}$

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Q 235 Marks Questions5 Marks

Prove that:
$\frac{\sin3\text{A}+\sin5\text{A}+\sin7\text{A}+\sin9\text{A}}{\cos3\text{A}+\cos5\text{A}+\cos7\text{A}\cos9\text{A}}=\tan6\text{A}$