Q1: If cotθ = 7/8 then what is the value of
Sol:
Q2: If tan A then find sin A.
Sol: In a right Δ ABC (∠B = 90°), Hypotenuse = AC, Base = AB, and Perpendicular = BC.
Since,
Using Pythagoras theorem, we have:
Q3: Evaluate cos 60°· sin 30° + sin 60°· cos 30°.
Sol: We have:
cos 60°· sin 30° + sin 60°· cos 30°
Q4: In the given figure, AC is the length of a ladder. Find it.
Sol: Let AC =x = [Length of ladder]
∴ In right Δ ABC,
Thus, the length of the ladder is 2√3 m.
Q5: If sin θ = 12/13 , find the value of: .
Sol:
Q6: In the given figure, find BC.
Sol: In Δ ABC,
Q7: 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
Q8: In the given figure, find AC, if AB = 12 cm.
Sol:
Q9: In the given figure, Δ ABC is a right triangle. Find the value of 2 sinθ − cosθ.
Sol: We have the right Δ ABC,
Q10: In the figure, find sinA.
Sol: In right Δ ABC,
Q11: Find the value of:
Sol: We have:
Q12: Write the value of:
Sol:
Q13: Write the value of:
Ans:
Q14: If sec^{2} θ (1 + sin θ) (1 − sinθ) = k, find the value of k.
Sol:
Q15: If sin then find the value of (2 cot^{2} θ + 2).
Sol: 2 cot^{2} θ + 2 = 2 (cot^{2} θ + 1) = 2 (cosec^{2} θ)
Q16: If cos A = 3/5, find 9 cot^{2} A − 1.
Q17: 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°
Q18: If sinθ = cosθ, find the value of θ.
Sol: We have:
sinθ = cosθ
Dividing both sides by cosθ, we get
⇒ tan θ = 1 ...(1)
From, the table, we have:
tan 45° = 1 ...(2)
From (1) and (2), we have:
θ = 45°.
Q19: If tan A = cot B, prove that A + B = 90°.
Sol: Since tan A = cot B
∴ tan A = tan (90°B)
⇒ A = 90°B
⇒ A + B = 90°. [Hence proved]
Q20: If sin 3θ = cos (θ – 6)° and 30 and (θ – 6)° are acute angles, find the value of θ.
Sol: We have:
sin 30 = cos (θ – 6)°
= sin [90° (θ – 6)°]
[∵ sin (90° – θ) = cos θ]
⇒ 3θ = 90° – (θ – 6)°
⇒ 3θ = 90 – θ + 6
⇒ 3θ + θ = 96
⇒ 4θ = 96
⇒ θ = = 24
Thus θ = 24°.
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1. What is trigonometry? 
2. Why is trigonometry important? 
3. What are the basic trigonometric ratios? 
4. How do you find the value of trigonometric ratios? 
5. What are the applications of trigonometry in real life? 

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