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

Q.1

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.2

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.3

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.4

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

29°
26°
23°
28°

Q.5

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.6

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.7

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.8

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

0
1
-1
2

Q.9

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

1
2
3
4

Q.10

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.11

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

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

Q.12

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.13

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

1
-1
2
0

Q.14

$$\frac{{{\text{cos }}\alpha }}{{{\text{sin }}\beta }} = n$$ 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.15

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

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

Q.16

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.17

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

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

Q.18

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.19

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.20

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

23°
37°
63°
67°

Q.21

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

23
24
25
26

Q.22

If tanA = n tanB and sinA = m sinB, then the value of cos²A = ?

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

Q.23

Evaluate : 3cos80°.cosec10° + 2cos59°.cosec31°

1
3
2
5

Q.24

The value of tan 4°.tan 43°.tan 47°.tan 86° is?

2
3
1
4

Q.25

$$\frac{{2{\text{sin }}{{68}^ \circ }}}{{{\text{cos 2}}{{\text{2}}^ \circ }}}$$ $$ - $$ $$\frac{{2{\text{cot 1}}{5^ \circ }}}{{5\tan {{75}^ \circ }}}$$ $$ - $$ $$\frac{{3\tan {{45}^ \circ }.\tan {{20}^ \circ }.\tan {{40}^ \circ }.\tan {{50}^ \circ }.\tan {{70}^ \circ }}}{5}$$ is equal to?

-1
0
1
2

Q.26

If x, y are acute angles, 0 < x + y < 90° and sin(2x - 20°) = cos(2y + 20°), then the value of tan(x + y) is?

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

Q.27

sin²5° + sin²6° + ............. sin²84° + sin²85° = ?

$$30\frac{1}{2}$$
$$40\frac{1}{2}$$
40
$$39\frac{1}{2}$$

Q.28

If A, B and C be the angles of a triangle, the incorrect relation is ?

$${\text{sin }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = {\text{cos}}\frac{{\text{C}}}{2}$$
$${\text{cos }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = {\text{sin}}\frac{{\text{C}}}{2}$$
$${\text{tan }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = \sec \frac{{\text{C}}}{2}$$
$${\text{cot }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = \tan \frac{{\text{C}}}{2}$$

Q.29

sin²5° + sin²10° + sin²15° + ...... sin²85° + sin²90° is equal to?

$${\text{7}}\frac{1}{2}$$
$${\text{8}}\frac{1}{2}$$
9
$$9\frac{1}{2}$$

Q.30

The value of tan 1°.tan 2°.tan 3° ............. tan 89° is?

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

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