If a 2 sec 2 x - b 2 tan 2 x = c 2 , then the value of sec 2 x + tan 2 x is equal to (assume b 2 ≠ a 2 )

$$\frac{{{b^2} + {a^2} - 2{c^2}}}{{{b^2} - {a^2}}}$$

$$\frac{{{b^2} - {a^2} + 2{c^2}}}{{{b^2} + {a^2}}}$$

$$\frac{{{b^2} - {a^2} - 2{c^2}}}{{{b^2} + {a^2}}}$$

$$\frac{{{b^2} - {a^2}}}{{{b^2} + {a^2} + 2{c^2}}}$$

Practice Trigonometry Multiple Choice Questions Quiz-2

Q.1

If rsinθ = 1, rcosθ = $$\sqrt 3 {\text{,}}$$ then the value of r²tanθ is?

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

Q.2

If α + β = 90°, then the value of (1 - sin²α)(1 - cos²α) × (1 + cot²β)(1 + tan²β) is?

1
-1
0
2

Q.3

$$\frac{{{\text{tan}}\theta + \cot \theta }}{{{\text{tan}}\theta - \cot \theta }} = 2,$$ $$\left( {0 \leqslant \theta \leqslant {{90}^ \circ }} \right),$$ then the value of $$\sin \theta $$ is?

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

Q.4

sin²θ - 3sinθ +2 = 0, will be true if ?

0 ≤ θ ≤ 90°
0 < θ < 90°
θ = 0°
θ = 90°

Q.5

If 2(cos²θ - sin²θ) = 1, (θ is positive acute angle), then cotθ is equal to?

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

Q.6

If tanθ + cotθ = 2, then the value if tan¹⁰⁰θ + cot¹⁰⁰θ is?

2
0
1
$$\sqrt 3 $$

Q.7

The value of, $${\text{sec}}\theta \left( {\frac{{1 + \sin \theta }}{{{\text{cos}}\theta }} + \frac{{{\text{cos}}\theta }}{{1 + \sin \theta }}} \right)$$ - $$2{\text{ta}}{{\text{n}}^2}\theta $$ is?

Q.8

If $${\text{tan }}{9^ \circ } = \frac{p}{q}{\text{,}}$$ then the value of $$\frac{{{\text{se}}{{\text{c}}^2}{\text{8}}{{\text{1}}^ \circ }}}{{1 + {{\cot }^2}{{81}^ \circ }}}$$ is?

$$\frac{p}{q}$$
1
$$\frac{{{p^2}}}{{{q^2}}}$$
$$\frac{{{q^2}}}{{{p^2}}}$$

Q.9

The value of following is, cos24° + cos55° + cos125° + cos204° + cos300° ?

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

Q.10

If 7sin²θ + 3cos²θ = 4, (0° ≤ θ ≤ 90°), then the value of θ is?

$$\frac{\pi }{2}$$
$$\frac{\pi }{3}$$
$$\frac{\pi }{6}$$
$$\frac{\pi }{4}$$

Q.11

The value of the expression: sin²1° + sin²11° + sin²21° + sin²31° + sin²41° + sin²45° + sin²49° + sin²59° + sin²69° + sin²79° + sin²89° is?

0
$${\text{5}}\frac{1}{2}$$
$${\text{4}}\frac{1}{2}$$
5

Q.12

If cos20° = m and cos70° =n, then the value of m² + n² is?

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

Q.13

If xtan60° + cos45° = sec45°, then the value of x² + 1 is?

$$\frac{6}{7}$$
$$\frac{7}{6}$$
$$\frac{5}{6}$$
$$\frac{6}{5}$$

Q.14

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

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

Q.15

If tan15° = 2 - $$\sqrt 3 ,$$ then the value of tan15° cot75° + tan75° cot15° is?

Q.16

If A = tan11°. tan29°, B = 2cot61°. cot79° then -

A = 2B
A = -2B
2A = B
2A = -B

Q.17

If $$\sin \alpha + \cos \beta = 2;$$ $$\left( {{0^ \circ } \leqslant \beta < \alpha \leqslant {{90}^ \circ }} \right){\text{,}}$$ then $${\text{sin}}\,{\left( {\frac{{2\alpha + \beta }}{3}} \right)^ \circ }$$ is?

$${\text{sin }}\frac{\alpha }{2}$$
$$\cos \frac{\alpha }{3}$$
$${\text{sin }}\frac{\alpha }{3}$$
$$\cos \frac{{2\alpha }}{3}$$

Q.18

If $$2\sin \left( {\frac{{\pi x}}{2}} \right) = {x^2} + \frac{1}{{{x^2}}}{\text{,}}$$ then the value of $$\left( {x - \frac{1}{x}} \right)$$ is?

-1
2
1
0

Q.19

If secA + tanA = a, then the value of cosA is?

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

Q.20

If sinP + cosecP = 2, then the value of sin⁷P + cosec⁷P is?

Q.21

If tan(2θ + 45°) = cot3θ, where (2θ + 45°) and 3θ are acute angles, then the value of θ is?

5°
9°
12°
15°

Q.22

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

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

Q.23

If $${\text{sin A}} - \cos {\text{A}}$$ = $$\frac{{\sqrt 3 - 1}}{2}{\text{,}}$$ then the value of $${\text{sin A}}.{\text{cosA}}$$ is?

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

Q.24

The value of the expression 2(sin⁶θ + cos⁶θ) - 3(sin⁴θ + cos⁴θ) + 1 is?

-1
0
1
2

Q.25

If a² sec²x - b² tan²x = c², then the value of sec²x + tan²x is equal to (assume b² ≠ a²)

$$\frac{{{b^2} - {a^2} + 2{c^2}}}{{{b^2} + {a^2}}}$$
$$\frac{{{b^2} + {a^2} - 2{c^2}}}{{{b^2} - {a^2}}}$$
$$\frac{{{b^2} - {a^2} - 2{c^2}}}{{{b^2} + {a^2}}}$$
$$\frac{{{b^2} - {a^2}}}{{{b^2} + {a^2} + 2{c^2}}}$$

Q.26

If tan⁴θ + tan²θ = 1, then the value of cos⁴θ + cos²θ is?

2
0
1
-1

Q.27

If $${\text{tan}}\left( {\frac{\pi }{2} - \frac{\theta }{2}} \right) = \sqrt 3 $$ the value of cosθ is?

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

Q.28

$$\sqrt {\frac{{1 + {\text{sin }}\theta }}{{1 - {\text{sin }}\theta }}} $$ + $$\sqrt {\frac{{1 - {\text{sin }}\theta }}{{1 + {\text{sin }}\theta }}} $$ is equal to?

2cosθ
2sinθ
2cotθ
2secθ

Q.29

If $${\left( {r\cos \theta - \sqrt 3 } \right)^2}$$ + $${\left( {r\sin \theta - 1} \right)^2}$$ = 0, then the value of $$\frac{{r\tan \theta + \sec \theta }}{{r\sec \theta + \tan \theta }}$$ is equal to?

$$\frac{4}{5}$$
$$\frac{3}{5}$$
$$\frac{{\sqrt 3 }}{4}$$
$$\frac{{\sqrt 5 }}{4}$$

Q.30

If x = cosecθ - sinθ and y = secθ - cosθ, then the relation between x and y is?

x² + y² + 3 = 1
x²y²(x² + y² + 3) = 1
x²(x² + y² - 5) = 1
y²(x² + y² - 5) = 1

If rsinθ = 1, rcosθ = $$\sqrt 3 {\text{,}}$$ then the value of r2tanθ is?

If α + β = 90°, then the value of (1 - sin2α)(1 - cos2α) × (1 + cot2β)(1 + tan2β) is?

$$\frac{{{\text{tan}}\theta + \cot \theta }}{{{\text{tan}}\theta - \cot \theta }} = 2,$$ $$\left( {0 \leqslant \theta \leqslant {{90}^ \circ }} \right),$$ then the value of $$\sin \theta $$ is?

sin2θ - 3sinθ +2 = 0, will be true if ?

If 2(cos2θ - sin2θ) = 1, (θ is positive acute angle), then cotθ is equal to?

If tanθ + cotθ = 2, then the value if tan100θ + cot100θ is?