Class 10 Practice – Level 3 – Set 2 – Trigonometry

Total questions: 15

Evaluate $ \displaystyle {{\left( {\dfrac{{\sin {{{49}}^{\circ }}}}{{\cos {{{41}}^{\circ }}}}} \right)}^{2}}+{{\left( {\frac{{\cos {{{41}}^{\circ }}}}{{\sin {{{49}}^{\circ }}}}} \right)}^{2}}$.

Topic: Trigonometric Identities and Simplification

-1

None

Evaluate $ \displaystyle \dfrac{{2\sin {{{68}}^{\circ }}}}{{\cos {{{22}}^{\circ }}}}-\dfrac{{2\cot {{{15}}^{\circ }}}}{{5\tan {{{75}}^{\circ }}}}-\dfrac{{3\tan {{{45}}^{\circ }}\tan {{{20}}^{\circ }}\tan {{{40}}^{\circ }}\tan {{{50}}^{\circ }}\tan {{{70}}^{\circ }}}}{5}$.

Topic: Evaluation of Trigonometric Expressions

None

If A, B and C are the angles of a △ABC, then find tan $ \displaystyle \left( {\frac{{\text{C}+\text{A}}}{2}} \right)$.

Topic: Trigonometric Ratios in a Triangle

$ \displaystyle\tan \dfrac{\text{B}}{2}$

$ \displaystyle\cot \dfrac{\text{B}}{2}$

$ \displaystyle cosec \dfrac{\text{B}}{2}$

$ \displaystyle\cos \dfrac{\text{B}}{2}$

None

Evaluate $ \displaystyle \dfrac{2}{3}\cos e{{c}^{2}}{{58}^{\circ }}-\dfrac{2}{3}\cot {{58}^{\circ }}\tan {{32}^{\circ }}-\dfrac{5}{3}\tan {{13}^{\circ }}\tan {{37}^{\circ }}\tan {{45}^{\circ }}\tan {{53}^{\circ }}\tan {{77}^{\circ }}$.

Topic: Trigonometric Simplifications

-1

None

If acosθ + bsinθ = m and asinθ − bcosθ = n, then (m² + n²) will be equal to:

Topic: Secant and Cosecant

(a² + b²)

(2a² + 3b²)

(a² + 2b²)

(3a² + b²)

None

If x = cosecA + cos A and y = cosecA − cosA, then $ \displaystyle {{\left( {\dfrac{2}{{x+y}}} \right)}^{2}}\left( {\dfrac{{x-y}}{2}} \right)-1$ will be equal to:

Topic: Secant and Cosecant

-1

None

If sin θ = $ \displaystyle \dfrac{3}{4}$, then find $ \displaystyle \sqrt{{\dfrac{{\text{cose}{{\text{c}}^{2}}\theta -{{{\cot }}^{2}}\theta }}{{{{{\sec }}^{2}}\theta -1}}}}$.

Topic: Trigonometric Functions

$ \displaystyle\dfrac{{\sqrt{7}}}{3}$

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

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

None

If sec θ = $ \displaystyle \dfrac{5}{4}$, then find $ \displaystyle \left( {\dfrac{{\sin \theta -2\cos \theta }}{{\tan \theta -\cos \theta }}} \right)$.

Topic: Secant and Cosecant

$ \displaystyle\dfrac{{12}}{7}$

$ \displaystyle\dfrac{{12}}{5}$

$ \displaystyle\dfrac{{14}}{5}$

$ \displaystyle\dfrac{{17}}{7}$

None

If sin$ \displaystyle a$ = $ \displaystyle \dfrac{1}{2}$, then find (3cosa − 4cos³$ \displaystyle a$).

Topic: Trigonometric Identities

-1

None

10.

Evaluate $ \displaystyle {{\sin }^{2}}\theta +\dfrac{1}{{1+{{{\tan }}^{2}}\theta }}$.

Topic: Trigonometric Identities

-1

None

11.

Evaluate $ \displaystyle {{\tan }^{2}}\theta -\dfrac{1}{{{{{\cos }}^{2}}\theta }}$.

Topic: Trigonometric Identities

-1

-2

None

12.

Evaluate $ \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{{cosec }^{2}}\theta$

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

None

13.

Evaluate sec$ \displaystyle \theta $(1 − sin$ \displaystyle \theta $)(sec$ \displaystyle \theta $ + tan$ \displaystyle \theta $).

Topic: Simplification of Trigonometric Expressions

−1

-2

None

14.

If sec2A = cosec(A − 45°), where 2A is an acute angle, then what is the value of A?

Topic: Trigonometric Equation

22°

33°

44°

55°

None

15.

What is the value of sec² $ \displaystyle \theta $(1 + sin$ \displaystyle \theta $)(1 − sin$ \displaystyle \theta $)?

Topic: Simplification of Trigonometric Expressions

−1

-2

None

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Class 10 Practice – Level 3 – Set 2 – Trigonometry

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