Practice Trigonometry Multiple Choice Questions Quiz-3 - MCQGeeks.com

Q.1

If $$\cot \theta = 4{\text{,}}$$ then the value of $$\frac{{5\sin \theta + 3\cos \theta }}{{5\sin \theta - 3\cos \theta }}$$ is?

$$ - \frac{{17}}{7}$$
$$\frac{1}{3}$$
3
9

Q.2

If $$\frac{{{{\sec }^2}{{70}^ \circ } - {\text{co}}{{\text{t}}^2}{{20}^ \circ }}}{{2\left( {{\text{cose}}{{\text{c}}^2}{{59}^ \circ } - {{\tan }^2}{{31}^ \circ }} \right)}}$$ = $$\frac{2}{m}{\text{,}}$$ then m is equal to?

2
3
4
1

Q.3

The value of 8(sin⁶θ + cos⁶θ) - 12(sin⁴θ + cos⁴θ) is equal to?

20
-20
-4
4

Q.4

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.5

If 1 + cos²θ = 3sinθ cosθ, then the integral value of cotθ is $$\left( {0 < \theta < \frac{\pi }{2}} \right) = \,?$$

2
1
3
0

Q.6

The expression of $$\frac{{\cot \theta + \operatorname{cosec} \theta - 1}}{{\cot \theta + \operatorname{cosec} \theta + 1}}$$ is equal to?

$$\frac{{1 + \cos \theta }}{{\sin \theta }}$$
$$\frac{{1 - \cos \theta }}{{\sin \theta }}$$
$$\frac{{\cot \theta + 1}}{{\operatorname{cosec} \theta }}$$
$$\frac{{\cot \theta - 1}}{{\sin \theta }}$$

Q.7

$$\frac{{\sin \theta + \cos \theta }}{{{\text{sin}}\theta - \cos \theta }} = 3,$$ then the value of $${\sin ^4}\theta - {\text{co}}{{\text{s}}^4}\theta $$ is?

$$\frac{1}{5}$$
$$\frac{3}{5}$$
$$\frac{2}{5}$$
$$\frac{4}{5}$$

Q.8

If secθ + tanθ = m(>1), then the value of sinθ is (0° < θ < 90°)

$$\frac{{1 - {m^2}}}{{1 + {m^2}}}$$
$$\frac{{{m^2} - 1}}{{{m^2} + 1}}$$
$$\frac{{{m^2} + 1}}{{{m^2} - 1}}$$
$$\frac{{1 + {m^2}}}{{1 - {m^2}}}$$

Q.9

Let A, B, C, D be the angles of a quadrilateral. If they are concyclic, then the value of cos A + cos B + cos C + cos D is ?

0
1
-1
2

Q.10

If $${\text{cos}}\theta = \frac{{{x^2} - {y^2}}}{{{x^2} + {y^2}}}$$ then the value of$${\text{cot}}\theta $$ is equal to $$\left[ {{\text{if }}{0^ \circ } \leqslant \theta \leqslant {{90}^ \circ }} \right]$$

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

Q.11

If sin 3A = cos(A - 26°), where 3A is an acute angle then the value of A is?

29°
26°
23°
28°

Q.12

If sin(θ + 18°) = cos60° (0° < θ < 90°), then the value of cos 5θ is?

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

Q.13

If θ be acute angle and tan(4θ - 50°) = cot(50° - θ), then the value of θ in degrees is?

30°
40°
50°
20°

Q.14

The value of the following is : $$\frac{{{{\left( {\tan {{20}^ \circ }} \right)}^2}}}{{{{\left( {{\text{cosec 7}}{0^ \circ }} \right)}^2}}}$$ $$ + $$ $$\frac{{{{\left( {\cot {{20}^ \circ }} \right)}^2}}}{{{{\left( {{\text{sec 7}}{0^ \circ }} \right)}^2}}}$$ $$ + $$ $$2\tan {15^ \circ }$$ . $$\tan {45^ \circ }$$ . $$\tan {75^ \circ }$$

1
2
4
3

Q.15

The value of tan10°. tan15°. tan75°. tan80° is?

0
1
-1
2

Q.16

If sin7x = cos11x, then the value of tan9x + cot9x is?

1
2
3
4

Q.17

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.18

The value of $$\left( {{{\sin }^2}7{{\frac{1}{2}}^ \circ } + {{\sin }^2}82{{\frac{1}{2}}^ \circ }} \right)$$ is?

1
2
0
4

Q.19

The value of sin²65° + sin²25° + cos²35° + cos²55° is?

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

Q.20

If $$\theta $$ is a positive acute angle and $$\tan 2\theta .\tan 3\theta $$ = 1 then the value of $$\left( {{\text{2co}}{{\text{s}}^2}\frac{{5\theta }}{2} - 1} \right)$$ is?

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

Q.21

If sinα .sec(30° + α) = 1, (0 < α < 60°), then the value of sinα + cos2α is?

1
$$\frac{{2 + \sqrt 3 }}{{2\sqrt 3 }}$$
0
$$\sqrt 2 $$

Q.22

If ∠A and ∠B are complementary to each other, then the value of sec²A + sec²B - sec²A.sec²B is?

1
-1
2
0

Q.23

$$\frac{{{\text{cos }}\alpha }}{{{\text{sin }}\beta }} = n$$ and $$\frac{{{\text{cos }}\alpha }}{{{\text{cos }}\beta }} = m,$$ then the value of $${\text{co}}{{\text{s}}^2}\beta $$ is?

$$\frac{{{m^2} - 1}}{{{n^2} - 1}}$$
$$\frac{{{m^2} - 3}}{{{n^2} - 4}}$$
$$\frac{{{m^2} + 3}}{{{n^2} + 3}}$$
$$\frac{{{n^2}}}{{{m^2} + {n^2}}}$$

Q.24

If tan7θ.tan2θ = 1, then the value of tan3θ is?

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

Q.25

If $${\text{sin}}\left( {{{60}^ \circ } - \theta } \right)$$ = $${\text{cos}}\left( {\psi - {{30}^ \circ }} \right),$$ then the value of $${\text{tan}}\left( {\psi - \theta } \right)$$ is (assume that $$\theta $$ and $$\psi $$ are both positive acute angles with$$\theta < {60^ \circ }$$ and $$\psi > {30^ \circ }$$ ) ?

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

Q.26

The value of cot 10°.cot 20°.cot 60°.cot 70°.cot 80° is?

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

Q.27

The value of cot 18° $$\left( {{\text{cot 7}}{{\text{2}}^ \circ }{\text{.co}}{{\text{s}}^2}{{22}^ \circ } + \frac{1}{{{\text{tan 7}}{{\text{2}}^ \circ }.{\text{se}}{{\text{c}}^2}{{68}^ \circ }}}} \right)$$ is?

1
$$\sqrt 2 $$
3
$$\frac{1}{{\sqrt 3 }}$$

Q.28

The value of cotθ.tan(90° - θ) - sec(90° - θ)cosecθ + (sin²25° + sin²65°) + $$\sqrt 3 $$ (tan5°. tan15°. tan30°. tan75°. tan85°)

1
-1
2
0

Q.29

If cosθ.cosec23° = 1, the value of θ is?

23°
37°
63°
67°

Q.30

If tanθ + cotθ = 5, then tan²θ + cot²θ is?

23
24
25
26

0 h : 0 m : 1 s