Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Class 10 Mathematics by VP Classes

Class 10 : Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

The document Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev is a part of the Class 10 Course Class 10 Mathematics by VP Classes.
All you need of Class 10 at this link: Class 10

VERY SHORT ANSWER TYPE QUESTIONS

Q1. If cotθ = 7/8 then what is the value of Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev
Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q2. If tan A  Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev then find sin A.

Sol. In a right Δ ABC (∠B = 90°), Hypotenuse = AC, Base = AB and Perpendicular = BC.
Since,

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Using Pythagoras theorem, we have:

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev
Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q3. Evaluate cos 60°· sin 30° + sin 60°· cos 30°.

Sol. We have:

cos 60°· sin 30° + sin 60°· cos 30°

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q4. If tan A = cot B, prove that A + B = 90°.

Sol. ∵ tan A = cot B
∴ tan A = tan (90° − B)
⇒ A = 90° − B
⇒ A + B = 90°.


Q5. Express sin 67° + cos 75° in terms of ratios of angles between 0° and 45°.
 Sol. 
∵ 67° = 90° − 23° and 75° = 90° − 15° 

∴ sin 67° + cos 75° = sin (90° − 23°) + cos (90° − 15°)  = cos 23° + sin 15°.


Q6. In the given figure, AC is the length of a ladder. Find it.

Sol. Let AC =x = [Length of ladder]
∴ In right Δ ABC,

  Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Thus, the length of the ladder is 2√3 m 


Q7. If sin θ = 12/13 , find the value of:  Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q8. In the given figure, find BC.

Sol. In Δ ABC,

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q9. In Δ ABC, if AD ⊥ BC and BD = 10 cm; ∠ B = 60° and ∠C = 30°, then find CD.

Sol. In right Δ ABD, we have

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q10. In the given figure, Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev  ind AC, if AB = 12 cm.

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q11. In the given figure, Δ ABC is a right triangle. Find the value of 2 sinθ − cosθ.
 Sol.
We have right Δ ABC,

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev
Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev
Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q12. In the figure, find sinA.

Sol. In right Δ ABC,

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q13. What is the value of sinθ. cos(90° − θ) + cosθ . sin(90° − θ)?

Sol. sinθ · cos(90° − θ) + cosθ · sin(90° − θ) = sinθ · sinθ + cosθ · cosθ
[∵ cos(90° − θ) = sinθ , sin(90° − θ) = cos θ]
= sin2 θ + cos2 θ
= 1


Q14. Show that: tan 10° tan 15° tan 75° tan 80° = 1

Sol. We have:

L.H.S. = tan 10° tan 15° tan 75° tan 80° =
tan (90° − 80°) tan 15° tan (90° − 15°) tan 80°
= cot 80° tan 15 cot 15° tan 80° = (cot 80° × tan 80°) × (tan 15° × cot 15°)
= 1× 1
= 1 = R.H.S.


Q15. Find the value of:

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Sol. We have:

  Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q16. Write the value of:  Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q17. Write the value of:   Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q18. If sec2 θ (1 + sin θ) (1 − sinθ) = k, find the value of k.

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q19. If sin Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev  then find the value of (2 cot2 θ + 2).

Sol. 2 cot2 θ + 2 = 2 (cot2 θ + 1) = 2 (cosec2 θ)

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q20. If cos A = 3/5, find 9 cot2 A − 1.

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev
Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q21. If sin 3θ = cos (θ − 6)° and 3θ and (θ − 6)° are acute angles, find the value of θ.

Sol. We have:
sin3θ = cos(θ − 6)° = sin[90°−(θ − 6)°]         

∵ [sin (90° − θ) = cos θ]
⇒ 3θ = 90° − (θ − 6)°
⇒ 3θ = 90 − θ + 6
⇒ 3θ + θ = 96

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q22. If tan θ = cot (30° + θ ), find the value of θ .

Sol. We have:
tan θ = cot (30° + θ)
= tan [90° − (30° + θ)]
= tan [90° − 30° − θ]
= tan (60° − θ)
⇒ θ = 60° − θ
⇒ θ + θ = 60°

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev


Q23. If sinθ = cosθ , find the value of θ .

Sol. We have:
sinθ = cosθ
Dividing both sides by cosθ, we get

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

⇒ tan θ = 1 ...(1)
From , the table, we have:
tan 45° = 1 ...(2)
From (1) and (2), we have:
θ = 45°.

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Complete Syllabus of Class 10

Dynamic Test

Content Category

Related Searches

ppt

,

Free

,

Objective type Questions

,

video lectures

,

Extra Questions

,

study material

,

Important questions

,

practice quizzes

,

MCQs

,

past year papers

,

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

,

Exam

,

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

,

Sample Paper

,

Semester Notes

,

Viva Questions

,

mock tests for examination

,

shortcuts and tricks

,

pdf

,

Previous Year Questions with Solutions

,

Summary

,

Very Short Answer Type Questions- Introduction to Trigonometry Class 10 Notes | EduRev

;