Trigonometric Identities - Gujarat Board (GSEB) STD 10 Maths Questions

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

$\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}$ is equal to:

A
$\sec^2\text{A}$
B
$-1$
C
$\cot^2\text{A}$
✓
$\tan^2\text{A}$

Answer: D.

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

$2(\sin^6\theta+\cos^6\theta)-3(\sin^4\theta+\cos^4\theta)$ is equal to:

A
$0$
B
$1$
✓
$-1$
D
None of these.

Answer: C.

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

If $\text{a}\cos\theta+\text{b}\sin\theta=4\text{ and a}\sin\theta-\text{b}\cos\theta=3,$ then $a^2+ b^2= 0$

A
$7$
B
$12$
✓
$25$
D
None of these.

Answer: C.

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

If $\text{x}=\text{r}\sin\theta\cos\phi,\text{y}=\text{r}\sin\phi\text{ and z}=\text{r}\cos\theta,$ then:

✓
$ x^2+y^2+z^2=r^2 $
B
$ x^2+y^2-z^2=r^2 $
C
$ x^2-y^2+z^2=r^2 $
D
$ z^2+y^2-x^2=r^2 $

Answer: A.

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

$(\sec\text{A}+\tan\text{A})(1-\sin\text{A})=$

A
$\sec\text{A}$
B
$\sin\text{A}$
C
$\text{cosec A}$
✓
$\cos\text{A}$

Answer: D.

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Q 62 Marks Questions2 Marks

Prove the following trigonometric identities.
$\text{cos}^2\text{A}+\frac{1}{1+\cot^2\text{A}}=1$

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Q 72 Marks Questions2 Marks

Prove the following trigonometric identities.
$\sin^2\text{A}\cot^2\text{A}+\cos^2\text{A}\tan^2\text{A}=1$

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Q 82 Marks Questions2 Marks

What is the value of $\frac{\tan^2\theta-\sec^2\theta}{\cot^2\theta-\text{cosec}^2\theta}?$

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Q 92 Marks Questions2 Marks

Prove the following trigonometric identities.
$(1+\tan^2\theta)(1-\sin\theta)(1+\sin\theta)=1$

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Q 102 Marks Questions2 Marks

Prove the following trigonometric identities.
$\frac{1+\cos\theta-\sin^2\theta}{\sin\theta(1+\cos\theta)}=\cot\theta$

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Q 113 Marks Question3 Marks

Prove the following trigonometric identities.
$\frac{1+\cos\theta+\sin\theta}{1+\cos\theta-\sin\theta}=\frac{1+\sin\theta}{\cos\theta}$

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Q 123 Marks Question3 Marks

If $\cos\text{A}=\frac{7}{25},$ find is the value of $\tan\text{A}+\cot\text{A}$.

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Q 133 Marks Question3 Marks

Prove the following trigonometric identities.
$\frac{\cot\text{A}+\tan\text{B}}{\cot\text{B}+\tan\text{A}}=\cot\text{A}\tan\text{B}$

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Q 143 Marks Question3 Marks

If $\cot\theta=\frac{1}{\sqrt{3}},$ find the value of $\frac{1+\cos^2\theta}{2-\sin^2\theta}$.

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Q 153 Marks Question3 Marks

If $\text{cosec A}=\sqrt{2},$ find the value of $\frac{2\sin^2\text{A}+3\cot^2\text{A}}{4(\tan^2-\cos^2\text{A})}$.

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Q 164 Marks Questions4 Marks

Prove the following trigonometric identities.
If $\text{cosec }\theta-\sin\theta=\text{a}^3,\sec\theta-\cos\theta=\text{b}^3,$ prove that $a^2 b^2\left(a^2+b^2\right)=1$.

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Q 174 Marks Questions4 Marks

Prove the following trigonometric identities.
Given that: $(1+\cos\alpha)(1+\cos\beta)(1+\cos\gamma)=(1-\cos\alpha)(1-\cos\alpha)(1-\cos\beta)(1-\cos\gamma)$
Show that one of the values of each member of this equality is $\sin\alpha\sin\beta\sin\gamma.$

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Q 184 Marks Questions4 Marks

Prove the following trigonometric identities.
$\frac{\sin\text{A}}{\sec\text{A}+\tan\text{A}-1}+\frac{\cos\text{A}}{\text{cosec A}+\cot\text{A}-1}=1$

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Q 194 Marks Questions4 Marks

Prove the following trigonometric identities.
$\frac{\cot^2\text{A}(\sec\text{A}-1)}{1+\sin\text{A}}=\sec^2\text{A}\Big(\frac{1-\sin\text{A}}{1+\sin\text{A}}\Big)$

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Q 204 Marks Questions4 Marks

Prove the following trigonometric identities.
$\frac{\tan^2\text{A}}{1+\tan^2\text{A}}+\frac{\cot^2\text{A}}{1+\cot^2\text{A}}=1$

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Trigonometric Identities Maths - Trigonometric Identities

Trigonometric Identities question types

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