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

Q.1

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.2

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.3

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.4

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.5

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.6

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

0.4
0.5
0.6
0.8

Q.7

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.8

θ is the positive acute angle and sinθ - cosθ = 0, then the value of secθ + cosecθ is?

2
$$\sqrt 2 $$
$${\text{2}}\sqrt 2 $$
$${\text{3}}\sqrt 2 $$

Q.9

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.10

The value of (1 + cotθ - cosecθ)(1 + tanθ + secθ) is equal to?

1
2
0
-1

Q.11

If tanθ - cotθ = 0 find the value of sinθ + cosθ ?

0
1
$$\sqrt 2 $$
2

Q.12

If 0° < A < 90°, then the value of tan²A + cot²A - sec²A cosec²A is?

0
1
2
-2

Q.13

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?

4
1
2
0

Q.14

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.15

If sinα .sec(30° + α) = 1, (0 < α < 60°), then the value of sinα + cos2α is?

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

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