Trigonometric Functions Test 32

Result

Trigonometric Functions Test 32

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

If $cos\alpha+cos\beta+cos\gamma= 0= sin\alpha+sin\beta+sin\gamma$ then $cos2^n\alpha+cos2^n\beta+cos2^n\gamma=?$

A
$0$

B
$1$

C
$cos 2(\alpha+\beta+gamma)$

D
$3cos(\alpha+\beta+\gamma)$
Question 2
1 / -0

If $\cos 3x+\sin\left(2x-\dfrac{7\pi}{6}\right)=-2$ , then $x$ is equal to $\left(where\ m\in Z\right)$

A
$\dfrac{\pi}{3}\left(6m-1\right)$

B
$\dfrac{\pi}{3}\left(6m+1\right)$

C
$\dfrac{\pi}{3}\left(2m+1\right)$

D
$none\ of\ these$

Solution
Question 3
1 / -0

If ${ tan }^{ 2 }\theta +{ cot }^{ 2 }\theta =\frac { a }{ b-cos4\theta } +c$ (where defined) is satisfied for all $\theta$ , then the value of (a + b + c) is equal to $(a,b,c\in I)$

A
6

B
7

C
8

D
9

Solution
Question 4
1 / -0

If $sin({ cot }^{ -1 }(x+1)=cos({ tan }^{ -1 }x)$ , then x is equal to

A
$-\dfrac { 1 }{ 2 }$

B
$\dfrac { 1 }{ 2 }$

C
Zero

D
$\dfrac { 9 }{ 4 }$

Solution
Question 5
1 / -0

The value of $\sin{\left(\alpha+\beta\right)}$ is

A
$\dfrac{24}{25}$

B
$\dfrac{12}{13}$

C
$\dfrac{1}{25}$

D
$None\ of\ these$

Solution
Question 6
1 / -0

If $cos(\alpha +\beta )sin(\gamma +\delta )=cos(\alpha -\beta )sin(\gamma -\delta )$ then

A
$cot\alpha cot\beta cot\delta =cot\gamma$

B
$cot\beta cot\delta cot\gamma =cot\alpha$

C
$cot\alpha cot\gamma cot\delta =cot\beta$

D
$cot\alpha cot\beta cot\gamma =cot\delta$

Solution

$(\cos \alpha \cos \beta-\sin \alpha \sin \beta)(\sin y \cos \delta+\cos y \sin \delta)=$
$(\cos \alpha \cos \beta+\sin \alpha \sin \beta)(\sin y \cos \delta-\cos y \sin \delta)$
$\Rightarrow \quad 2 \cos \alpha \cos \beta \cos y \sin \delta=2$ sin $\alpha$ sin $\beta$ siny cos $\delta$
$=\dfrac{\cos \alpha}{\sin \alpha} \times \dfrac{\cos \beta}{\sin \beta} \times \dfrac{\cos y}{\sin y}=\dfrac{\cos \delta}{\sin \delta}$
$=\cot \alpha \cot \beta \cot y=\cot \delta$
$\therefore$ option $D$ is correct.
Question 7
1 / -0

In a $\triangle ABC, \sum a \cos A=4 \sin A \sin B \sin C$ , then value of $\left(\dfrac{\sum \sin A}{\sum a}\right)^{2}$ is-

A
$\dfrac{1}{4}$

B
$\dfrac{1}{2}$

C
$1$

D
$\dfrac{1}{3}$

Solution
Question 8
1 / -0

$sin\left( { 4tan }^{ -1 }{ \cfrac { 1 }{ 3 } } \right) =$

A
$\frac { 12 }{ 25 }$

B
$\frac { 24 }{ 25 }$

C
$\frac { 1 }{ 5 }$

D
none of these

Solution
Question 9
1 / -0

If $0 < \phi < \dfrac {\pi}{2}$ and if $\displaystyle x=\sum^{\alpha}_{n=0}\cos^{2}\phi:y=\sum^{\alpha}_{n=0}\sin^{2n}\phi$ then

A
$x^{2}+y^{2}=1$

B
$x^{2}-y^{2}=1$

C
$x+y=xy$

D
$\dfrac {1}{x}+\dfrac {1}{y}=1$

Solution
Question 10
1 / -0

The value of $\cos^2 \theta + \cos^2 \left(\dfrac{2\pi}{2} - \theta\right) + \cos^2 \left(\dfrac{2\pi}{3} + \theta \right)$ is

A
$$-\dfarc{3}{2}$$

B
$\dfrac{3}{2}$

C
$$\dfarc{1}{2}$$

D
$1$

Solution

$\begin{aligned} & \cos ^{2} \alpha+\cos ^{2}\left(\frac{2 \pi}{3}+\alpha\right)+\cos ^{2}\left(\frac{2 \pi}{3}-\alpha\right) \\ =& \cos ^{2} \alpha+\left(\cos \left(\frac{2 \pi}{3}\right) \cos \alpha-\sin \left(\frac{2 \pi}{3}\right) \sin \alpha\right)^{2} \\ &+\left(\cos \left(\frac{2 \pi}{3}\right) \cos \alpha+\sin \left(\frac{2 \pi}{3}\right) \sin \alpha\right)^{2} \\ &=\cos ^{2} \alpha+\left(\frac{-1}{2} \cos \alpha-\frac{\sqrt{3}}{2} \sin \alpha\right)^{2}+\left(\frac{-1}{2} \cos \alpha\right.\\ &\left.+\frac{\sqrt{3}}{2} \sin \alpha\right)^{2} \\ &=\cos ^{2} \alpha+\frac{1}{4} \cos ^{2} \alpha+\frac{3}{4} \sin ^{2} \alpha+\frac{\sqrt{3}}{2} \cos \alpha \sin \alpha \\ &+\frac{1}{4} \cos ^{2} \alpha+\frac{3}{4} \sin ^{2} \alpha-\frac{\sqrt{3}}{2} \cos \alpha \sin \alpha \\ &=\frac{3}{2} \cos ^{2} \alpha+\frac{3}{2} \sin ^{2} \alpha \\ &=\frac{3}{2}\left(\cos ^{2} \alpha+\sin ^{2} \alpha\right) \\ &=\frac{3}{2} \\ & \text { option } B \text { is correct } \end{aligned}$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Trigonometric Functions Test 32

Result

Trigonometric Functions Test 32

Score

-

Rank

-

SHARING IS CARING

Question 1

000

111

cos2(α+β+gamma)cos 2(\alpha+\beta+gamma)cos2(α+β+gamma)

3cos(α+β+γ)3cos(\alpha+\beta+\gamma)3cos(α+β+γ)

Question 2

π3(6m−1)\dfrac{\pi}{3}\left(6m-1\right)3π​(6m−1)

π3(6m+1)\dfrac{\pi}{3}\left(6m+1\right)3π​(6m+1)

π3(2m+1)\dfrac{\pi}{3}\left(2m+1\right)3π​(2m+1)

none of thesenone\ of\ thesenone of these

Solution

Question 3

6

7

8

9

Solution

Question 4

−12-\dfrac { 1 }{ 2 } −21​

12\dfrac { 1 }{ 2 } 21​

Zero

94\dfrac { 9 }{ 4 } 49​

Solution

Question 5

2425\dfrac{24}{25}2524​

1213\dfrac{12}{13}1312​

125\dfrac{1}{25}251​

None of theseNone\ of\ theseNone of these

Solution

Question 6

cotαcotβcotδ=cotγcot\alpha cot\beta cot\delta =cot\gamma cotαcotβcotδ=cotγ

cotβcotδcotγ=cotαcot\beta cot\delta cot\gamma =cot\alpha cotβcotδcotγ=cotα

cotαcotγcotδ=cotβcot\alpha cot\gamma cot\delta =cot\beta cotαcotγcotδ=cotβ

cotαcotβcotγ=cotδcot\alpha cot\beta cot\gamma =cot\delta cotαcotβcotγ=cotδ

Solution

Question 7

14\dfrac{1}{4}41​

12\dfrac{1}{2}21​

111

13\dfrac{1}{3}31​

Solution

Question 8

1225\frac { 12 }{ 25 } 2512​

2425\frac { 24 }{ 25 } 2524​

15\frac { 1 }{ 5 } 51​

none of these

Solution

Question 9

x2+y2=1x^{2}+y^{2}=1x2+y2=1

x2−y2=1x^{2}-y^{2}=1x2−y2=1

x+y=xyx+y=xyx+y=xy

1x+1y=1\dfrac {1}{x}+\dfrac {1}{y}=1x1​+y1​=1

Solution

Question 10

$$-\dfarc{3}{2}$$

32\dfrac{3}{2}23​

$$\dfarc{1}{2}$$

111

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.

$0$

$1$

$cos 2(\alpha+\beta+gamma)$

$3cos(\alpha+\beta+\gamma)$

$\dfrac{\pi}{3}\left(6m-1\right)$

$\dfrac{\pi}{3}\left(6m+1\right)$

$\dfrac{\pi}{3}\left(2m+1\right)$

$none\ of\ these$

$-\dfrac { 1 }{ 2 }$

$\dfrac { 1 }{ 2 }$

$\dfrac { 9 }{ 4 }$

$\dfrac{24}{25}$

$\dfrac{12}{13}$

$\dfrac{1}{25}$

$None\ of\ these$

$cot\alpha cot\beta cot\delta =cot\gamma$

$cot\beta cot\delta cot\gamma =cot\alpha$

$cot\alpha cot\gamma cot\delta =cot\beta$

$cot\alpha cot\beta cot\gamma =cot\delta$

$\dfrac{1}{4}$

$\dfrac{1}{2}$

$1$

$\dfrac{1}{3}$

$\frac { 12 }{ 25 }$

$\frac { 24 }{ 25 }$

$\frac { 1 }{ 5 }$

$x^{2}+y^{2}=1$

$x^{2}-y^{2}=1$

$x+y=xy$

$\dfrac {1}{x}+\dfrac {1}{y}=1$

$\dfrac{3}{2}$

$1$