If A = sin 2 θ + cos 4 θ for any value of θ, then the value of A is?

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

$${\text{1}} \leqslant {\text{A}} \leqslant {\text{1}}$$

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

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

Practice Trigonometry Multiple Choice Questions Quiz-5

Q.1

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

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

Q.2

If $$\sin \frac{{\pi x}}{2} = {x^2} - 2x + 2,$$ the value of x is?

0
1
-1
None of these

Q.3

The measure of the angles of a triangle are in the ratio 2 : 7 : 11. Measures of angles are ?

16°, 56°, 88°
18°, 63°, 99°
20°, 70°, 90°
25°, 175°, 105°

Q.4

If θ be an acute angle and 7sin²θ + 3cos²θ = 4, then the value of tanθ is?

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

Q.5

The numerical value of $$\frac{1}{{1 + {{\cot }^2}\theta }}$$ + $$\frac{3}{{1 + {\text{ta}}{{\text{n}}^2}\theta }}$$ + $$2{\sin ^2}\theta $$ will be?

Q.6

The value of cos1° cos2° cos3° ............. cos177° cos178° cos179° is?

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

Q.7

The angles of a triangle are (x + 5)°, (2x - 3)° and (3x + 4)°. Then the value of x is?

Q.8

The expression $$\frac{{\tan {{57}^ \circ } + \cot {{37}^ \circ }}}{{\tan {{33}^ \circ } + \cot {{53}^ \circ }}}$$ is equal to?

tan30° cot57°
tan57° cot37°
tan33° cot 53°
tan33° cot37°

Q.9

If tan θ = 1, then the value of $$\frac{{8\sin \theta + 5\cos \theta }}{{{{\sin }^3}\theta - 2{{\cos }^3}\theta + 7\cos \theta }}$$ is?

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

Q.10

The minimum value of 2sin²θ + 3cos²θ is ?

Q.11

Maximum value of (2sinθ + 3cosθ) is?

2
$$\sqrt {13} $$
$$\sqrt {15} $$
1

Q.12

The equation $${\cos ^2}\theta $$ = $$\frac{{{{\left( {x + y} \right)}^2}}}{{4xy}}$$ is only possible when ?

x = -y
x > y
x = y
x < y

Q.13

The greatest value of sin⁴θ + cos⁴θ is?

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

Q.14

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

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

Q.15

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.16

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.17

If θ is positive acute angle and 3(sec²θ + tan²θ) = 5, then the value of cos2θ is?

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

Q.18

If secθ + tanθ = 2 + $$\sqrt 5 {\text{,}}$$ then the value of sinθ + cosθ is?

$$\frac{3}{{\sqrt 5 }}$$
$$\sqrt 5 $$
$$\frac{7}{{\sqrt 5 }}$$
$$\frac{1}{{\sqrt 5 }}$$

Q.19

If $$sec\theta = x + \frac{1}{{4x}}$$ $$\left( {{0^ \circ } < \theta < {{90}^ \circ }} \right)$$ then $$sec\theta $$ + $${\text{tan}}\theta $$ is equal to?

$$\frac{x}{2}$$
2x
x
$$\frac{1}{{2x}}$$

Q.20

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.21

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

60°
30°
0°
90°

Q.22

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.23

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

-1
2
0
1

Q.24

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.25

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.26

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

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

Q.27

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.28

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.29

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.30

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

45°
90°
30°
60°