Class 10 Practice – Level 1 – Trigonometry

Total questions: 40

If $ \displaystyle {{\sec }^{2}}\theta \left( {1+\sin \theta } \right)\left( {1-\sin \theta } \right)=k$ find $ \displaystyle k$.

Topic: Trigonometric Identities

None

Taking θ = 30°, solve : $ \displaystyle 3\sin \theta -4{{\sin }^{3}}\theta $.

Topic: Simplification of Trigonometric Expressions

-1

None

Evaluate: cos60° ⋅ cos30° − sin60° ⋅ sin30°.

Topic: Trigonometric Formulae

–1

None

Find the value of $ \displaystyle 9{{\sec }^{2}}\text{A}-9{{\tan }^{2}}\text{A}$.

Topic: Secant and Tangent Identities

None

Find the value of $ \displaystyle \dfrac{{1+{{{\tan }}^{2}}\text{A}}}{{1+{{{\cot }}^{2}}\text{A}}}=$.

Topic: Trigonometric Simplifications

$ \displaystyle {{\sec }^{2}}\text{A}$

–1

$ \displaystyle {{{{\cot }}^{2}}\text{A}}$

$ \displaystyle {{\tan }^{2}}\text{A}$

None

Given that sin α = $ \displaystyle \dfrac{1}{2}$ and cosβ = $ \displaystyle \dfrac{1}{2}$, then the value of (α + β) is:

Topic: Sum of Angles in Trigonometry

0°

30°

60°

90°

None

Evaluate : cos60° cos30° + sin60° sin30°.

Topic: Trigonometric Formulae

$ \displaystyle {\dfrac{{\sqrt{3}}}{2}}$

$ \displaystyle {\dfrac{{\sqrt{3}}}{4}}$

None

What is the value of ' x ' in the following?

Topic: Trigonometric Equation

$ \displaystyle \sqrt{3}\tan 2x-3=0.$

30°

60°

90°

45°

None

In the given figure, What is the value of tan P − cot R?

Topic: Trigonometric Identities

-1

None of these

None

10.

If $ \displaystyle \cot \theta =\dfrac{7}{8},$ evaluate: $ \displaystyle {{\cot }^{2}}\theta $.

Topic: Basic Trigonometric Ratios

$ \displaystyle \dfrac{{36}}{{64}}$

$ \displaystyle \dfrac{{121}}{{64}}$

$ \displaystyle \dfrac{{81}}{{64}}$

$ \displaystyle \dfrac{{49}}{{64}}$

None

11.

If $ \displaystyle \cot \theta =\dfrac{9}{{40}},$ What is the values of $ \displaystyle \sec \theta $?

Topic: Trigonometric Ratios and Reciprocal Identities

$ \displaystyle \dfrac{{41}}{9}$

$ \displaystyle \dfrac{{40}}{9}$

$ \displaystyle \dfrac{{36}}{9}$

$ \displaystyle \dfrac{{26}}{5}$

None

12.

The value of (tan1° tan2° ……tan89° ) is equal to:

Topic: Product of Trigonometric Functions

None

13.

What is the value of (cos48° − sin42°)?

Topic: Trigonometric Simplifications

None

14.

What is the value of $ \displaystyle \left( {{{{\tan }}^{2}}{{{60}}^{\circ }}+{{{\sin }}^{2}}{{{45}}^{\circ }}} \right)$?

Topic: Trigonometric Values and Simplifications

$ \displaystyle \dfrac{1}{2}$

$ \displaystyle \dfrac{7}{2}$

$ \displaystyle \dfrac{3}{2}$

$ \displaystyle \dfrac{5}{2}$

None

15.

What is the value of A, when $ \displaystyle {{{{\tan }}^{2}}\text{A}}$ = cot(A − 24°)?

Topic: Trigonometric Equation

30°

40°

38°

52°

None

16.

What is the value of $ \displaystyle \left( {{{{\cos }}^{2}}{{{45}}^{\circ }}+{{{\cot }}^{2}}{{{45}}^{\circ }}} \right)$?

Topic: Trigonometric Simplifications

$ \displaystyle \dfrac{9}{2}$

$ \displaystyle \dfrac{7}{2}$

$ \displaystyle \dfrac{4}{2}$

$ \displaystyle \dfrac{3}{2}$

None

17.

What is the value of (tan27° − cot63°)?

Topic: Difference of Trigonometric Functions

None

18.

The value of sinθ + cosθ will be always:

Topic: Trigonometric Sum

more than or equal to 1

None

19.

What is the value of (cos48° − sin42°)?

Topic: Trigonometric Identities

None

20.

What is the value of (tan1° tan2° ……tan89°)?

Topic: Product of Trigonometric Functions

None

21.

If $ \displaystyle \sin \text{A }+{{\sin }^{2}}\text{A}=1\text{ }$, then what is the value of the expression $ \displaystyle \left( {{{{\cos }}^{2}}\text{A+}{{{\cos }}^{4}}\text{A}} \right)$?

Topic: Trigonometric Equation

None

22.

Evaluate value of : $ \displaystyle {{\sin }^{2}}{{60}^{\circ }}+2\tan {{45}^{\circ }}-{{\cos }^{2}}{{30}^{\circ }}$.

Topic: Evaluation of Trigonometric Expressions

None

23.

What is the value of $ \displaystyle \left( {{{{\cos }}^{2}}{{{67}}^{\circ }}-{{{\sin }}^{2}}{{{23}}^{\circ }}} \right)$?

Topic: Trigonometric Identities

None

24.

In the given figure, What is the value of tanP − cotR?

Topic: Trigonometric Ratio Simplification

None

25.

The value of cosθ increases as the value of θ increases.

Topic: Trigonometric Functions

True

False

Cannot be predicted

Incomplete information

None

26.

The value of sinθ increases as θ increases.

Topic: Trigonometric Functions

True

False

Cannot be predicted

Incomplete information

None

27.

What is the value of sinθcos(90°− θ) + cosθ sin(90° − θ)?

Topic: Trigonometric Identities

None

28.

In a right triangle ABC, right-angled at B, if tanA = 1, then what is the value of A that satisfies 2 sinA cosA = 1.

Topic: Trigonometric Ratios in Right Triangles

None

29.

In ΔABC, right-angled at B, AB = 5 cm and ∠ACB = 30° (see the figure). Determine the lengths of the sides BC and AC.

Topic: Trigonometric Ratios in Right Triangles

Trigonometric ratios of some specific angles

5 cm

10 cm

15 cm

20 cm

None

30.

In ΔPQR, right-angled at Q (see the figure), PQ = 3 cm and PR = 6 cm. Determine the value of ∠QPR and ∠PRQ.

Topic: Trigonometric Ratios in Right Triangles

20°, 70°

30°, 60°

50°, 90°

40°, 60°

None

31.

If sin(A − B) = $ \displaystyle \dfrac{1}{2}$, cos(A + B) = $ \displaystyle \dfrac{1}{2}$, 0° B, Then what is the value of A and B?

Topic: Trigonometric Identities and Equations

45°, 15°

55°, 20°

75°, 25°

50°, 90°

None

32.

Evaluate value of $ \displaystyle \frac{{\tan {{{65}}^{\circ }}}}{{\cot {{{25}}^{\circ }}}}$.

Topic: Trigonometric Ratio Simplification

None

33.

If sin3 A = cos(A − 26°), where 3 A is an acute angle, What should be the value of A?

Topic: Trigonometric Equation

30°

20°

29°

34°

None

34.

Express cot85° + cos75° in terms of trigonometric ratios of angles between 0° and 45°.

Topic: Complementary Angle Identities

cos5° + tan15°

tan5° + sin15°

tan5° + cot15°

sin5° + cot15°

None

35.

Find the value of sec A(1 − sin A)(sec A + tan A).

Topic: Trigonometric Identities

None

36.

Is it true or not $ \displaystyle \dfrac{{\cot \text{A}-\cos \text{A}}}{{\cot \text{A}+\cos \text{A}}}=\dfrac{{\text{cosec A}-1}}{{\text{cosec A}+1}}$?

Topic: Trigonometric Identities

True

False

Cannot be predicted

Incomplete information

None

37.

Find the value of $ \displaystyle \dfrac{1}{{1+\sin \theta }}+\dfrac{1}{{1-\sin \theta }}$.

Topic: Simplification of Trigonometric Expressions

$ \displaystyle 2{sec }^{2}\theta$

$ \displaystyle {sec }^{2}\theta$

$ \displaystyle 2{sec }^{3}\theta$

$ \displaystyle 4{sec }^{2}\theta$

None

38.

If $ \displaystyle \sin \theta +{{\sin }^{2}}\theta =1,$ then find $ \displaystyle {{\cos }^{2}}\theta +{{\cos }^{4}}\theta$.

Topic: Trigonometric Identities and Equations

-1

None

39.

Is it true or not $ \displaystyle {{\tan }^{4}}\theta +{{\tan }^{2}}\theta ={{\sec }^{4}}\theta -{{\sec }^{2}}\theta $?

Topic: Trigonometric Identities

True

False

Cannot be predicted

Incomplete information

None

40.

If tan 2 = cot(A − 18°), where 2 A is an acute angle, then what is the value of A?

Topic: Trigonometric Equation

28°

44°

36°

90°

None

1 out of 40

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Class 10 Practice – Level 1 – Trigonometry

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