Practice Trigonometry Multiple Choice Questions Quiz-7 - MCQGeeks.com

Q.1

If $$\sqrt 3 $$ tanθ = 3sinθ, then the value of (sin²θ - cos²θ) is?

1
3
$$\frac{1}{3}$$
None of these

Q.2

If a right-angled triangle XYZ right-angled at Y. If XY = $${\text{2}}\sqrt 6 $$ and XZ - YZ = 2, then secX + tanX is?

$$\frac{1}{{\sqrt 6 }}$$
$$\sqrt 6 $$
$$2\sqrt 6 $$
$$\frac{{\sqrt 6 }}{2}$$

Q.3

$$\frac{{2\sin \theta }}{{\cos \theta \left( {1 + {\text{ta}}{{\text{n}}^2}\theta } \right)}}$$ simplifies to?

cosθ
cos²θ
sin²θ
sinθ

Q.4

If $$\tan \theta = \frac{3}{4}{\text{,}}$$ find the value of $${\text{cos2}}\theta $$ ?

$$\frac{{24}}{{25}}$$
$$\frac{{16}}{{25}}$$
$$\frac{7}{{25}}$$
$$\frac{9}{{30}}$$

Q.5

The value of $$\frac{{{\text{sin 6}}{5^ \circ }}}{{\cos {{25}^ \circ }}}$$ is?

0
1
2
No defined

Q.6

If α + β = 90° and α : β = 2 : 1, then the ratio of cosα to cosβ is?

1 : $$\sqrt 3 $$
1 : 3
1 : $$\sqrt 2 $$
1 : 2

Q.7

If sinθ = $$\frac{a}{b}$$ then the value of secθ - cosθ is? (where 0° < θ < 90°)

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

Q.8

If secα + tanα = 2, then the value of sinα is (assume that 0 < α < 90°)

0.4
0.5
0.6
0.8

Q.9

If $$\theta $$ be acute angle and $$\cos \theta = \frac{{15}}{{17}}{\text{,}}$$ then the value of $${\text{cot}}\left( {{{90}^ \circ } - \theta } \right)$$ is?

$$\frac{{2\sqrt 8 }}{{15}}$$
$$\frac{8}{{15}}$$
$$\frac{{\sqrt 2 }}{{17}}$$
$$\frac{{8\sqrt 2 }}{{17}}$$

Q.10

In ΔABC, ∠B = 90° and AB : BC = 2 : 1, then value of (sinA + cotC) = ?

$$3 + \sqrt 5 $$
$$\frac{{2 + \sqrt 5 }}{{2\sqrt 5 }}$$
$$2 + \sqrt 5 $$
$$3\sqrt 5 $$

Q.11

In a triangle ABC, ∠ABC = 75° and ∠ACB = $$\frac{{{\pi ^c}}}{4},$$ the circular measure of ∠BAC is?

$$\frac{{5\pi }}{{12}}$$ radian
$$\frac{\pi }{3}$$ radian
$$\frac{\pi }{6}$$ radian
$$\frac{\pi }{2}$$ radian

Q.12

If $$6{\sin ^4}\theta + 3{\cos ^4}\theta = 2{\text{,}}$$ then the value of $${\left[ {7{{\operatorname{cosec} }^6}\theta + 8{{\sec }^6}\theta } \right]^{\frac{1}{3}}}$$ is?

2
4
8
6

Q.13

If sin21° = $$\frac{x}{y}{\text{,}}$$ then sec21° - sin69° is equal to?

$$\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }}$$
$$\frac{{{y^2}}}{{x\sqrt {{y^2} - {x^2}} }}$$
$$\frac{{{x^2}}}{{y\sqrt {{x^2} - {y^2}} }}$$
$$\frac{{{y^2}}}{{x\sqrt {{x^2} - {y^2}} }}$$

Q.14

If cos27° = x, then the value of tan63° is?

$$\frac{x}{{\sqrt {1 - {x^2}} }}$$
$$\frac{x}{{\sqrt {1 + {x^2}} }}$$
$$\frac{{\sqrt {1 - {x^2}} }}{x}$$
$$\frac{{\sqrt {1 + {x^2}} }}{x}$$

Q.15

If sin31° = $$\frac{x}{y}{\text{,}}$$ then the value of sec31° - sin59° is?

$$\frac{{{x^2}}}{{y\sqrt {{y^2} + {x^2}} }}$$
$$\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }}$$
$$ - \frac{{{y^2}}}{{\sqrt {{y^2} - {x^2}} }}$$
$$ - \frac{{{x^2}}}{{\sqrt {{y^2} - {x^2}} }}$$

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