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Quiz 6
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Q.1
The value of sec
4
A(1 - sin
4
A) - 2tan
2
A is?
$$\frac{1}{2}$$
0
2
1
Q.2
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.3
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.4
If in a triangle ABC, sinA = cosB then the value of cosC is?
$$\frac{{\sqrt 3 }}{2}$$
0
1
$$\frac{1}{{\sqrt 2 }}$$
Q.5
If $$\sec \theta - \tan \theta = \frac{1}{{\sqrt 3 }}{\text{,}}$$ the value of $$\sec \theta $$ . $$\tan \theta $$ = ?
$$\frac{4}{{\sqrt 3 }}$$
$$\frac{2}{{\sqrt 3 }}$$
$$\frac{2}{3}$$
$$\frac{1}{{\sqrt 3 }}$$
Q.6
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.7
If sec15θ = cosec15θ (0° < θ < 10°) then the value of θ is?
9°
5°
8°
3°
Q.8
If θ is positive acute angle and 7cos
2
θ + 3sin
2
θ = 4, then value of θ is?
60°
30°
45°
90°
Q.9
The least value of tan
2
x + cot
2
x is?
3
2
0
1
Q.10
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.11
If sinθ × cosθ = $$\frac{1}{2}{\text{,}}$$ Then the value of sinθ - cosθ is where 0° < θ < 90°.
0
$$\sqrt 2 $$
2
1
Q.12
The value of cos
2
20° + cos
2
70° = ?
$$\sqrt 2 $$
1
$$\frac{1}{3}$$
2
Q.13
The value of (cosec a - sin a)(sec a - cos a)(tan a + cot a) is?
4
6
2
1
Q.14
The value of θ(0 ≤ θ ≤ 90°) satisfying 2sin
2
θ = 3cosθ is?
60°
90°
30°
45°
Q.15
a, b, c are the lengths of three sides of a triangle ABC. If a, b, c are related by the relation a
2
+ b
2
+ c
2
= ab + bc + ca, then the value of (sin
2
A + sin
2
B + sin
2
C) is?
$$\frac{3}{4}$$
$$\frac{3}{2}$$
$$\frac{{3\sqrt 3 }}{2}$$
$$\frac{9}{4}$$
Q.16
If tanθ = tan30° .tan60° and θ is an acute angle, then 2θ is equal to?
30°
45°
90°
0°
Q.17
If 7sin
2
θ + 3cos
2
θ = 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
Q.18
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.19
If cos
2
x + cos
4
x = 1, then tan
2
x + tan
4
x = ?
0
1
2tan
2
x
2tan
4
x
Q.20
Find the value of, 8cos10°. cos20°. cos40° = ?
2cot20°
4tan10°
1
cot10°
Q.21
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.22
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.23
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.24
Find the value of sin
2
25° + sin
2
65° + coses
2
57° - tan
2
33° = ?
1
2
3
0
Q.25
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.26
The value of coses
2
60° + sec
2
60° - cot
2
60° + tan
2
30° will be?
5
$${\text{5}}\frac{1}{2}$$
$${\text{5}}\frac{2}{3}$$
$${\text{5}}\frac{1}{3}$$
Q.27
In a ΔABC, if 4∠A = 3∠B = 12∠C, find ∠A?
22.5°
90°
67.5°
112.5°
Q.28
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.29
The value of $${\text{cot1}}{{\text{7}}^ \circ }$$ $$\left( {\cot {{73}^ \circ }\,{{\cos }^2}{{22}^ \circ }\, + \frac{1}{{\cot {{17}^ \circ }se{c^2}{{68}^ \circ }}}} \right)$$ is?
0
1
27
$$\sqrt 3 $$
Q.30
θ is the positive acute angle and sinθ - cosθ = 0, then the value of secθ + cosecθ is?
2
$$\sqrt 2 $$
$${\text{2}}\sqrt 2 $$
$${\text{3}}\sqrt 2 $$
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