Practice Trigonometry Multiple Choice Questions Quiz-6 - MCQGeeks.com

Q.1

The value of $$\left( {\frac{{\sin \theta + \sin \phi }}{{\cos \theta + \cos \phi }} + \frac{{\cos \theta - \cos \phi }}{{\sin\theta - \sin\phi }}} \right)$$ is?

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

Q.2

If cos²x + cos⁴x = 1, then tan²x + tan⁴x = ?

0
1
2tan²x
2tan⁴x

Q.3

Find the value of, 8cos10°. cos20°. cos40° = ?

2cot20°
4tan10°
1
cot10°

Q.4

The value of $${\text{se}}{{\text{c}}^2}{17^ \circ }$$ - $$\frac{1}{{{\text{ta}}{{\text{n}}^2}{{73}^ \circ }}}$$ - $$\sin {17^ \circ }$$ $$\sec {73^ \circ }$$ is?

1
0
-1
2

Q.5

If $${\text{tan }}\alpha = 2,$$ then the value of $$\frac{{{\text{cose}}{{\text{c}}^2}\alpha - {\text{se}}{{\text{c}}^2}\alpha }}{{{\text{cose}}{{\text{c}}^2}\alpha + se{c^2}\alpha }}$$ is?

$$ - \frac{5}{9}$$
$$\frac{3}{5}$$
$$ - \frac{3}{5}$$
$$\frac{{17}}{5}$$

Q.6

Find the value of sin²25° + sin²65° + coses²57° - tan²33° = ?

1
2
3
0

Q.7

If $${\text{tan}}\theta = \frac{4}{3}{\text{,}}$$ then the value of $$\frac{{3\sin \theta + 2\cos \theta }}{{3\sin \theta - 2\cos \theta }}$$ is?

$$\frac{1}{2}$$
$${\text{1}}\frac{2}{3}$$
3
-3

Q.8

The value of coses²60° + sec²60° - cot²60° + tan²30° will be?

5
$${\text{5}}\frac{1}{2}$$
$${\text{5}}\frac{2}{3}$$
$${\text{5}}\frac{1}{3}$$

Q.9

In a ΔABC, if 4∠A = 3∠B = 12∠C, find ∠A?

22.5°
90°
67.5°
112.5°

Q.10

If θ is a acute angle and sin(θ + 18°) = $$\frac{1}{2}{\text{,}}$$ then the value of θ in circular measure is?

$$\frac{\pi }{{12}}$$ Radians
$$\frac{\pi }{{15}}$$ Radians
$$\frac{{2\pi }}{5}$$ Radians
$$\frac{{3\pi }}{{13}}$$ Radians

Q.11

If $$\sqrt 3 $$ tanθ = 3sinθ, then the value of (sin²θ - cos²θ) is?

1
3
$$\frac{1}{3}$$
None of these

Q.12

If a right-angled triangle XYZ right-angled at Y. If XY = $${\text{2}}\sqrt 6 $$ and XZ - YZ = 2, then secX + tanX is?

$$\frac{1}{{\sqrt 6 }}$$
$$\sqrt 6 $$
$$2\sqrt 6 $$
$$\frac{{\sqrt 6 }}{2}$$

Q.13

$$\frac{{2\sin \theta }}{{\cos \theta \left( {1 + {\text{ta}}{{\text{n}}^2}\theta } \right)}}$$ simplifies to?

cosθ
cos²θ
sin²θ
sinθ

Q.14

If $$\tan \theta = \frac{3}{4}{\text{,}}$$ find the value of $${\text{cos2}}\theta $$ ?

$$\frac{{24}}{{25}}$$
$$\frac{{16}}{{25}}$$
$$\frac{7}{{25}}$$
$$\frac{9}{{30}}$$

Q.15

The value of $$\frac{{{\text{sin 6}}{5^ \circ }}}{{\cos {{25}^ \circ }}}$$ is?

0
1
2
No defined

Q.16

If α + β = 90° and α : β = 2 : 1, then the ratio of cosα to cosβ is?

1 : $$\sqrt 3 $$
1 : 3
1 : $$\sqrt 2 $$
1 : 2

Q.17

If $$\theta $$ be acute angle and $$\cos \theta = \frac{{15}}{{17}}{\text{,}}$$ then the value of $${\text{cot}}\left( {{{90}^ \circ } - \theta } \right)$$ is?

$$\frac{{2\sqrt 8 }}{{15}}$$
$$\frac{8}{{15}}$$
$$\frac{{\sqrt 2 }}{{17}}$$
$$\frac{{8\sqrt 2 }}{{17}}$$

Q.18

In ΔABC, ∠B = 90° and AB : BC = 2 : 1, then value of (sinA + cotC) = ?

$$3 + \sqrt 5 $$
$$\frac{{2 + \sqrt 5 }}{{2\sqrt 5 }}$$
$$2 + \sqrt 5 $$
$$3\sqrt 5 $$

Q.19

In a triangle ABC, ∠ABC = 75° and ∠ACB = $$\frac{{{\pi ^c}}}{4},$$ the circular measure of ∠BAC is?

$$\frac{{5\pi }}{{12}}$$ radian
$$\frac{\pi }{3}$$ radian
$$\frac{\pi }{6}$$ radian
$$\frac{\pi }{2}$$ radian

Q.20

If $$6{\sin ^4}\theta + 3{\cos ^4}\theta = 2{\text{,}}$$ then the value of $${\left[ {7{{\operatorname{cosec} }^6}\theta + 8{{\sec }^6}\theta } \right]^{\frac{1}{3}}}$$ is?

2
4
8
6

Q.21

If sin21° = $$\frac{x}{y}{\text{,}}$$ then sec21° - sin69° is equal to?

$$\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }}$$
$$\frac{{{y^2}}}{{x\sqrt {{y^2} - {x^2}} }}$$
$$\frac{{{x^2}}}{{y\sqrt {{x^2} - {y^2}} }}$$
$$\frac{{{y^2}}}{{x\sqrt {{x^2} - {y^2}} }}$$

Q.22

If cos27° = x, then the value of tan63° is?

$$\frac{x}{{\sqrt {1 - {x^2}} }}$$
$$\frac{x}{{\sqrt {1 + {x^2}} }}$$
$$\frac{{\sqrt {1 - {x^2}} }}{x}$$
$$\frac{{\sqrt {1 + {x^2}} }}{x}$$

Q.23

If sin31° = $$\frac{x}{y}{\text{,}}$$ then the value of sec31° - sin59° is?

$$\frac{{{x^2}}}{{y\sqrt {{y^2} + {x^2}} }}$$
$$\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }}$$
$$ - \frac{{{y^2}}}{{\sqrt {{y^2} - {x^2}} }}$$
$$ - \frac{{{x^2}}}{{\sqrt {{y^2} - {x^2}} }}$$

Q.24

If $$\theta $$ is a positive acute angle and $${\text{4}}{\sin ^2}\theta $$ = 3, then the value of $${\text{tan}}\theta $$ - $$\cot \frac{\theta }{2}$$ is?

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

Q.25

If sinθ + cosθ = $$\sqrt 2 $$ sin(90° - θ) then the value of cotθ is?

-$$\sqrt 2 $$ - 1
$$\sqrt 2 $$ + 1
$$\sqrt 2 $$ - 1
-$$\sqrt 2 $$ + 1

Q.26

If A = tan11°. tan29°, B = 2cot61°. cot79° then -

A = 2B
A = -2B
2A = B
2A = -B

Q.27

If $$\frac{{{\text{sec}}\theta + {\text{tan}}\theta }}{{{\text{sec}}\theta - {\text{tan}}\theta }} = 2\frac{{51}}{{79}}{\text{,}}$$ then the value of $$\sin \theta $$ is?

$$\frac{{91}}{{144}}$$
$$\frac{{39}}{{72}}$$
$$\frac{{65}}{{144}}$$
$$\frac{{35}}{{72}}$$

Q.28

The value of the following is : $${\left( {\frac{{{\text{sin 4}}{{\text{7}}^ \circ }}}{{\cos {{43}^ \circ }}}} \right)^2}$$ + $${\left( {\frac{{\cos {{43}^ \circ }}}{{{\text{sin }}{{47}^ \circ }}}} \right)^2}$$ - $$4{\text{co}}{{\text{s}}^2}{45^ \circ }$$ = ?

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

Q.29

If tan²θ = 1 - e², then the value of secθ + tan³θ.cosecθ is?

$${\left( {2 + {e^2}} \right)^2}$$
$${\left( {2 - {e^2}} \right)^{\frac{1}{2}}}$$
$${\left( {2 + {e^2}} \right)^{\frac{1}{2}}}$$
$${\left( {2 - {e^2}} \right)^{\frac{3}{2}}}$$

Q.30

If $$x = a{\text{ }}\sec \theta .\cos \phi ,$$ $$y = b{\text{ }}\sec \theta .\sin \phi ,$$ $$z = c{\text{ tan}}\theta {\text{.}}$$ then the value of $$\frac{{{x^2}}}{{{a^2}}}$$ + $$\frac{{{y^2}}}{{{b^2}}}$$ - $$\frac{{{z^2}}}{{{c^2}}}$$ is?

1
4
9
0

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