TRIGONOMETRIC FUNCTIONS - Gujarat Board (GSEB) STD 11 Science MATHS Questions

Q 1MCQ1 Mark

If $\text{cosec x}+\cot \text{x}=\frac{11}{2},$ then $\tan\text{x}$ is equal to:

A
$\frac{21}{22}$
B
$\frac{15}{16}$
✓
$\frac{44}{117}$
D
$\frac{117}{44}$

Answer: C.

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Q 2MCQ1 Mark

The smallest value of x satisfying the equation $\sqrt{3}(\cot\text{x}+\tan\text{x})=4$ is:

A
$\frac{2\pi}{3}$
B
$\frac{\pi}{3}$
✓
$\frac{\pi}{6}$
D
$\frac{\pi}{12}$

Answer: C.

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Q 3MCQ1 Mark

$\sec^2\text{x}=\frac{4\text{xy}}{(\text{x}+\text{y})^2}$ is true if and only if

A
$\text{x+y}\neq0$
✓
$\text{x=y, x}\neq0$
C
$\text{x=y}$
D
$\text{x}\neq0,\text{y}\neq0$

Answer: B.

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Q 4MCQ1 Mark

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

A
$\cot\frac{\alpha}{2}$
B
$\cot\alpha$
✓
$\tan\frac{\alpha}{2}$
D
None of these

Answer: C.

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Q 5MCQ1 Mark

If in $\text{a}\triangle\text{ABC},\tan\text{B}+\tan\text{C}=6,$ then $\cot\text{A}\cot\text{B}\cot\text{C}=$

A
$6$
B
$1$
✓
$\frac16$
D
None of these

Answer: C.

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Q 6(Each question 1 marks)1 Mark

Find the general solution for the equation: sinx + sin 3x + sin 5x = 0

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Q 7(Each question 1 marks)1 Mark

Find the general solution for $\sec ^2 2 x=1-\tan 2 x$ equation.

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Q 8(Each question 1 marks)1 Mark

Find the general solution for the equation: sin 2x + cos x = 0

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Q 9(Each question 1 marks)1 Mark

Find the general solution for the equation: cos 3x + cos x – cos 2x = 0

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Q 10(Each question 1 marks)1 Mark

Find the general solution for the equation: cos 4x = cos 2x

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Q 11(Each question 2 marks)2 Marks

Prove that : $\frac { ( \sin 7 x + \sin 5 x ) + ( \sin 9 x + \sin 3 x ) } { ( \cos 7 x + \cos 5 x ) + ( \cos 9 x + \cos 3 x ) } = \tan 6 x$

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Q 12(Each question 2 marks)2 Marks

Prove that : sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x

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Q 13(Each question 2 marks)2 Marks

Prove that: $(\cos x-\cos y)^{2}+(\sin x-\sin y)^{2}=4 \sin ^{2} \frac{x-y}{2}$

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Q 14(Each question 2 marks)2 Marks

Prove that : $(\cos x+\cos y)^2+(\sin x-\sin y)^2 = 4{\cos ^2}\frac{{x + y}}{2}$

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Q 15(Each question 2 marks)2 Marks

Prove that : (sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0

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Q 16(Each question 3 marks)3 Marks

Find sin $\frac{x}{2},\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in the $\cos\;x\;=-\frac13$, x in quadrant III.

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Q 17(Each question 3 marks)3 Marks

Find sin $\frac{x}{2},\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in the $\tan x = - \frac{4}{3}$, x in quadrant II.

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Q 18(Each question 3 marks)3 Marks

Prove that : sin 3x + sin 2x - sin x $ = 4\sin \;x\cos \frac{x}{2}\cos \frac{{3x}}{2}$

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Q 19(Each question 3 marks)3 Marks

Find sin $\frac{x}{2},\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in the $\sin x = \frac{1}{4}$, x in quadrant II.

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Q 20(Each question 3 marks)3 Marks

Prove that: $\cos 6 x=32 \cos ^6 x-48 \cos ^4 x+18 \cos ^2 x-1$

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Q 21(Each question 4 marks)4 Marks

Find the general solution for each of the following equations: $\sin2\text{x}+\cos\text{x}=0$

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Q 22(Each question 4 marks)4 Marks

Prove the following: $\sin2\text{x}+2\sin4\text{x}+\sin6\text{x}=4\cos^2\text{x}\sin4\text{x}$

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Q 23(Each question 4 marks)4 Marks

Prove the following: $\cos\Big(\frac{3\pi}{4}+\text{x}\Big)-\cos\Big(\frac{3\pi}{4}-\text{x}\Big)=-\sqrt{2}\sin\text{x}$

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Q 24(Each question 4 marks)4 Marks

Prove the following: $\sin(\text{n}+1)\text{x}\sin(\text{n}+2)\text{x}+2\cos(\text{n}+1)\text{x}\cos(\text{n}+2)\text{x}=\cos\text{x}$

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Q 25(Each question 4 marks)4 Marks

Prove the following: $\cot4\text{x}(\sin5\text{x}+\sin3\text{x})=\cot4\text{x}(\sin5\text{x}-\sin3\text{x})$

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TRIGONOMETRIC FUNCTIONS question types

TRIGONOMETRIC FUNCTIONS questions

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TRIGONOMETRIC FUNCTIONS MATHS - TRIGONOMETRIC FUNCTIONS

TRIGONOMETRIC FUNCTIONS question types

TRIGONOMETRIC FUNCTIONS questions

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