Practice Trigonometry Multiple Choice Questions Quiz-5 - MCQGeeks.com

Q.1

Which one of the following is true for 0° < θ < 90° ?

cosθ ≤ cos²θ
cosθ < cos²θ
cosθ > cos²θ
cosθ ≥ cos²θ

Q.2

ABCD is a rectangle of which AC is a diagonal. The value of (tan² ∠CAD + 1)sin² ∠BAC is?

2
$$\frac{1}{4}$$
1
0

Q.3

If A is an acute angle and cotA + cosecA = 3, then the value of sinA is?

1
$$\frac{4}{5}$$
$$\frac{3}{5}$$
0

Q.4

If $${\text{2cos}}\theta - \sin \theta = \frac{1}{{\sqrt 2 }},$$ $$\left( {{0^ \circ } < \theta < {{90}^ \circ }} \right)$$ the value of $$2\sin \theta $$ + $$\cos \theta $$ is?

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

Q.5

If sec²θ + tan²θ = 7, then the value of θ when 0° ≤ θ ≤ 90° is?

60°
30°
0°
90°

Q.6

If the sum and difference of two angles are 135° and $$\frac{\pi }{{12}}$$ respectively, then the value of the angles in degree measure are?

70°, 65°
75°, 60°
45°, 90°
80°, 55°

Q.7

If cosx + cos²x = 1,the numerical value of (sin¹² + 3sin¹⁰x + 3sin⁸x + sin⁶x - 1) = ?

-1
2
0
1

Q.8

The simplified value of (sec x sec y + tan x tan y)² - (sec x tan y + tan x sec y)²

-1
0
sec² x
1

Q.9

If A = sin²θ + cos⁴θ for any value of θ, then the value of A is?

$${\text{1}} \leqslant {\text{A}} \leqslant {\text{1}}$$
$$\frac{3}{4} \leqslant {\text{A}} \leqslant {\text{1}}$$
$$\frac{{13}}{{16}} \leqslant {\text{A}} \leqslant {\text{1}}$$
$$\frac{3}{4} \leqslant {\text{A}} \leqslant \frac{{13}}{{16}}$$

Q.10

If cosθ + sinθ = $$\sqrt 2 $$ cosθ, then cosθ - sinθ is?

$$\sqrt 2 $$ tanθ
-$$\sqrt 2 $$ cosθ
-$$\sqrt 2 $$ sinθ
$$\sqrt 2 $$ sinθ

Q.11

If $$\sin \left( {\theta + {{30}^ \circ }} \right) = \frac{3}{{\sqrt {12} }}{\text{,}}$$ then find $${\text{co}}{{\text{s}}^2}\theta ?$$

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

Q.12

If $${\text{0}} \leqslant \theta \leqslant {90^ \circ }$$ and $$4{\cos ^2}\theta $$ - $$4\sqrt 3 \cos \theta $$ + 3 = 0 then the value of $$\theta $$ is?

30°
90°
45°
60°

Q.13

In circular measure, the value of the angle 11° 15' is?

$$\frac{{{\pi ^c}}}{{16}}$$
$$\frac{{{\pi ^c}}}{8}$$
$$\frac{{{\pi ^c}}}{4}$$
$$\frac{{{\pi ^c}}}{{12}}$$

Q.14

If sec(4x - 50°) = cosec(50° - x), then the value of x is?

45°
90°
30°
60°

Q.15

The value of sec⁴A(1 - sin⁴A) - 2tan²A is?

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

Q.16

If $${\text{co}}{{\text{s}}^4}\theta - {\sin ^4}\theta = \frac{2}{3}{\text{,}}$$ then the value of $${\text{2co}}{{\text{s}}^2}\theta - 1$$ is?

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

Q.17

If $$\pi \sin \theta = 1,$$ $$\pi \cos \theta = 1{\text{,}}$$ then the value of $$\left\{ {\sqrt 3 \tan \left( {\frac{2}{3}\theta } \right) + 1} \right\}$$ is?

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

Q.18

If in a triangle ABC, sinA = cosB then the value of cosC is?

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

Q.19

If $$\frac{{\cos \theta }}{{1 - \sin \theta }}$$ + $$\frac{{\cos \theta }}{{1 + {\text{sin }}\theta }}$$ = 4, then the value of $$\theta \left( {{0^ \circ } < \theta < {{90}^ \circ }} \right)$$ is?

60°
45°
30°
35°

Q.20

If sec15θ = cosec15θ (0° < θ < 10°) then the value of θ is?

9°
5°
8°
3°

Q.21

If θ is positive acute angle and 7cos²θ + 3sin²θ = 4, then value of θ is?

60°
30°
45°
90°

Q.22

The least value of tan²x + cot²x is?

3
2
0
1

Q.23

If $$\sin \theta - \cos \theta = \frac{7}{{13}}$$ and $${0^ \circ }{\text{ < }}\theta {\text{ < }}{90^ \circ }{\text{,}}$$ then the value of $$\sin \theta $$ + $${\text{cos}}\theta $$ is?

$$\frac{{17}}{{13}}$$
$$\frac{{13}}{{17}}$$
$$\frac{1}{{13}}$$
$$\frac{1}{{17}}$$

Q.24

If sinθ × cosθ = $$\frac{1}{2}{\text{,}}$$ Then the value of sinθ - cosθ is where 0° < θ < 90°.

0
$$\sqrt 2 $$
2
1

Q.25

The value of cos²20° + cos²70° = ?

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

Q.26

The value of (cosec a - sin a)(sec a - cos a)(tan a + cot a) is?

4
6
2
1

Q.27

The value of θ(0 ≤ θ ≤ 90°) satisfying 2sin²θ = 3cosθ is?

60°
90°
30°
45°

Q.28

a, b, c are the lengths of three sides of a triangle ABC. If a, b, c are related by the relation a² + b² + c² = ab + bc + ca, then the value of (sin²A + sin²B + sin²C) is?

$$\frac{3}{4}$$
$$\frac{3}{2}$$
$$\frac{{3\sqrt 3 }}{2}$$
$$\frac{9}{4}$$

Q.29

If tanθ = tan30° .tan60° and θ is an acute angle, then 2θ is equal to?

30°
45°
90°
0°

Q.30

If 7sin²θ + 3cos²θ = 4, then the value of secθ + cosecθ is?

$$\frac{2}{{\sqrt 3 }} - 2$$
$$\frac{2}{{\sqrt 3 }} + 2$$
$$\frac{2}{{\sqrt 3 }}$$
None of these

0 h : 0 m : 1 s