If tanA = n tanB and sinA = m sinB, then the value of cos 2 A = ?

$$\frac{{{m^2} - 1}}{{{n^2} - 1}}$$

$$\frac{{{m^2} + 1}}{{{n^2} + 1}}$$

$$\frac{{{m^2} + 1}}{{{n^2} - 1}}$$

$$\frac{{{m^2} - 1}}{{{n^2} + 1}}$$

If tan 2 θ = 1 - e 2 , then the value of secθ + tan 3 θ.cosecθ is?

$${\left( {2 - {e^2}} \right)^{\frac{3}{2}}}$$

$${\left( {2 + {e^2}} \right)^2}$$

$${\left( {2 - {e^2}} \right)^{\frac{1}{2}}}$$

$${\left( {2 + {e^2}} \right)^{\frac{1}{2}}}$$

Practice Trigonometry Multiple Choice Questions Quiz-4

Q.1

If tanA = n tanB and sinA = m sinB, then the value of cos²A = ?

$$\frac{{{m^2} + 1}}{{{n^2} + 1}}$$
$$\frac{{{m^2} + 1}}{{{n^2} - 1}}$$
$$\frac{{{m^2} - 1}}{{{n^2} - 1}}$$
$$\frac{{{m^2} - 1}}{{{n^2} + 1}}$$

Q.2

Evaluate : 3cos80°.cosec10° + 2cos59°.cosec31°

Q.3

The value of tan 4°.tan 43°.tan 47°.tan 86° is?

Q.4

$$\frac{{2{\text{sin }}{{68}^ \circ }}}{{{\text{cos 2}}{{\text{2}}^ \circ }}}$$ $$ - $$ $$\frac{{2{\text{cot 1}}{5^ \circ }}}{{5\tan {{75}^ \circ }}}$$ $$ - $$ $$\frac{{3\tan {{45}^ \circ }.\tan {{20}^ \circ }.\tan {{40}^ \circ }.\tan {{50}^ \circ }.\tan {{70}^ \circ }}}{5}$$ is equal to?

-1
0
1
2

Q.5

If x, y are acute angles, 0 < x + y < 90° and sin(2x - 20°) = cos(2y + 20°), then the value of tan(x + y) is?

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

Q.6

sin²5° + sin²6° + ............. sin²84° + sin²85° = ?

$$30\frac{1}{2}$$
$$40\frac{1}{2}$$
40
$$39\frac{1}{2}$$

Q.7

If A, B and C be the angles of a triangle, the incorrect relation is ?

$${\text{sin }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = {\text{cos}}\frac{{\text{C}}}{2}$$
$${\text{cos }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = {\text{sin}}\frac{{\text{C}}}{2}$$
$${\text{tan }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = \sec \frac{{\text{C}}}{2}$$
$${\text{cot }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = \tan \frac{{\text{C}}}{2}$$

Q.8

sin²5° + sin²10° + sin²15° + ...... sin²85° + sin²90° is equal to?

$${\text{7}}\frac{1}{2}$$
$${\text{8}}\frac{1}{2}$$
9
$$9\frac{1}{2}$$

Q.9

The value of tan 1°.tan 2°.tan 3° ............. tan 89° is?

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

Q.10

If tan²θ = 1 - e², then the value of secθ + tan³θ.cosecθ is?

$${\left( {2 + {e^2}} \right)^2}$$
$${\left( {2 - {e^2}} \right)^{\frac{1}{2}}}$$
$${\left( {2 + {e^2}} \right)^{\frac{1}{2}}}$$
$${\left( {2 - {e^2}} \right)^{\frac{3}{2}}}$$

Q.11

If $$\frac{{{\text{cos }}\alpha }}{{{\text{cos }}\beta }} = a$$ and $$\frac{{{\text{sin }}\alpha }}{{{\text{sin }}\beta }} = b{\text{,}}$$ then the value of $${\sin ^2}\beta $$ in terms of a and b is?

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

Q.12

The elimination of θ from x cosθ - y sinθ = 2 and x sinθ + y cosθ = 4 will give?

x² + y² = 20
3x² + y² = 20
x² - y² = 20
3x² - y² = 10

Q.13

The value of $$\left[ {\frac{{{\text{co}}{{\text{s}}^2}{\text{A}}\left( {{\text{sin A}} + {\text{cos A}}} \right)}}{{{\text{cose}}{{\text{c}}^2}{\text{A}}\left( {{\text{sin A}} - {\text{cos A}}} \right)}} + \frac{{{\text{si}}{{\text{n}}^2}{\text{A}}\left( {{\text{sin A}} - {\text{cos A}}} \right)}}{{{\text{se}}{{\text{c}}^2}{\text{A}}\left( {{\text{sin A}} + {\text{cos A}}} \right)}}} \right]$$ $$\left( {{\text{se}}{{\text{c}}^2}{\text{ A}} - {\text{cose}}{{\text{c}}^2}{\text{ A}}} \right) = ?$$

Q.14

2cosec²23° cot²67° - sin²23° - sin²67° - cot²67° is equal to?

1
sec²23°
tan²23°
0

Q.15

$$\frac{{{\text{tan}}\theta }}{{1 - {\text{cot}}\theta }}{\text{ + }}\frac{{{\text{cot}}\theta }}{{1 - {\text{tan}}\theta }}$$ is equal to?

1 - tanθ - cotθ
tanθ - cotθ +1
cotθ - tanθ + 1
tanθ + cotθ + 1

Q.16

The value of $$\frac{{\cot {{30}^ \circ } - \cot {{75}^ \circ }}}{{\tan {{15}^ \circ } - \tan {{60}^ \circ }}}$$ is?

0
1
$$\sqrt 3 - 1$$
-1

Q.17

If $${\text{se}}{{\text{c}}^2}\theta + {\text{ta}}{{\text{n}}^2}\theta = \frac{7}{{12}}{\text{,}}$$ then $${\text{se}}{{\text{c}}^4}\theta $$ - $${\text{ta}}{{\text{n}}^4}\theta $$ = ?

$$\frac{7}{{12}}$$
$$\frac{1}{2}$$
$$\frac{7}{2}$$
1

Q.18

sinθ = 0.7 then cosθ, 0 ≤ θ < 90° is?

0.3
$$\sqrt {0.49} $$
$$\sqrt {0.51} $$
$$\sqrt {0.9} $$

Q.19

If $${\text{2}}\sin \theta + {\text{cos}}\theta = \frac{7}{3}{\text{,}}$$ then the value of $$\left( {{\text{ta}}{{\text{n}}^2}\theta - {{\sec }^2}\theta } \right)$$ is?

0
-1
$$\frac{3}{7}$$
$$\frac{7}{3}$$

Q.20

The value of $${\sec ^2}\theta $$ - $$\frac{{{{\sin }^2}\theta - 2{{\sin }^4}\theta }}{{{\text{2co}}{{\text{s}}^4}\theta - {\text{co}}{{\text{s}}^2}\theta }}$$ is?

1
2
-1
0

Q.21

If θ be a positive acute angle satisfying cos²θ + cos⁴θ = 1, then the value of tan²θ + tan⁴θ is?

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

Q.22

If $${\text{co}}{{\text{s}}^4}\theta - {\sin ^4}\theta = \frac{2}{3},$$ then the value of $${\text{1}} - {\text{2}}{\sin ^2}\theta $$ is?

$$\frac{4}{3}$$
0
$$\frac{2}{3}$$
$$\frac{1}{3}$$

Q.23

The value of $$\frac{{{\text{sin A}}}}{{1 + \cos {\text{ A}}}}$$ + $$\frac{{{\text{sin A}}}}{{1 - \cos {\text{ A}}}}$$ is $$\left( {{0^ \circ } < {\text{A}} < {{90}^ \circ }} \right)$$

2 cosec A
2 sec A
2 sin A
2 cos A

Q.24

If $$\cos \pi x = {x^2} - x + \frac{5}{4}{\text{,}}$$ then the value of x will be ?

0
1
-1
None of the above

Q.25

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

1
2
0
-1

Q.26

If $$x = a{\text{ }}\sec \theta .\cos \phi ,$$ $$y = b{\text{ }}\sec \theta .sin\phi ,$$ $$z = c{\text{ tan}}\theta {\text{.}}$$ then the value of $$\frac{{{x^2}}}{{{a^2}}}$$ + $$\frac{{{y^2}}}{{{b^2}}}$$ - $$\frac{{{z^2}}}{{{c^2}}}$$ is?

Q.27

The numerical value of $$\frac{5}{{{\text{se}}{{\text{c}}^2}\theta }}$$ + $$\frac{2}{{1 + {\text{co}}{{\text{t}}^2}\theta }}$$ + $${\text{3}}{\sin ^2}\theta $$ is?

Q.28

The numerical value of $$\left( {\frac{1}{{\cos \theta }} + \frac{1}{{\cot \theta }}} \right)$$ $$\left( {\frac{1}{{\cos \theta }} - \frac{1}{{\cot \theta }}} \right)$$ is?

0
-1
1
2

Q.29

If $${\text{tan}}\theta = \frac{4}{3}{\text{,}}$$ then the value of $$\frac{{3\sin \theta + 2{\text{cos}}\theta }}{{3\sin \theta - 2{\text{cos}}\theta }}$$ is?

0.5
-0.5
3.0
-3.0

Q.30

The simplified value of (secA - cosA)² + (cosecA - sinA)² - (cotA - tanA)²

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

If tanA = n tanB and sinA = m sinB, then the value of cos2A = ?