In Worksheet on finding the unknown angle using Trigonometric identities we will solve various types of practice questions on solving equation.
Here you will get 11 different types of solving equation using trigonometric identities questions with some selected questions hints.
1. Solve the equation 2 cos2 θ = 1; where 0° < θ < 90°.
2. Solve the equation \(\sqrt{3}\) tan θ = 1; where 0° < θ < 90°.
3. Solve the equation 2 cos (2θ) = 1; where 0° < θ < 90°.
4. Solve the equation 2 cos2 θ - 11 cos θ + 5 = 0; where 0° < θ < 90°.
5. Solve the equation 2 sin2 θ + cos θ - 2 = 0; where 0° < θ < 90°.
6. Solve the equation 2 sec2 θ = 5 tan θ; where 0° < θ < 90°.
Hint: 2 sec2 θ = 5 tan θ
⟹ 2 (1 + tan2 θ) = 5 tan θ
⟹ 2 + 2 tan2 θ = 5 tan θ
⟹ 2 tan2 θ - 5 tan θ + 2 = 0
⟹ 2 tan2 θ - 4 tan θ - tan θ + 2 = 0
⟹ 2 tan θ (tan θ – 2) – 1 (tan θ – 2) = 0
⟹ (tan θ – 2)(2 tan θ – 1) = 0
7. Are the following identities? If not, solve for θ, where 0°
< θ < 90°).
(i) \(\frac{ cos θ}{1 - sin θ}\) + \(\frac{ cos θ}{1 + sin θ}\) = 4
(i) \(\frac{ cos θ}{csc θ + 1}\) + \(\frac{ cos θ}{csc θ - 1}\) = 2.
8. Solve: 2 sin A – 1 = 0. Hence, prove that sin (3A) = 3 sin A – 4 sin3 A.
9. If 2 cos θ - \(\sqrt{3}\) = 0, find the value of θ.
Also, prove that sin (2θ) = 2 sin θ ∙ cos θ.
10. If 9 sin θ + 40 cos θ = 41, prove that 41 cos θ = 40.
11. If tan θ + sec θ = 3, where θ is acute then prove that 5 sin θ = 4.
Hint: tan θ + sec θ = 3
⟹ \(\frac{sin θ}{cos θ}\) + \(\frac{1}{cos θ}\) = 3
⟹ \(\frac{sin θ + 1}{cos θ}\) = 3
⟹ sin θ + 1 = 3 cos θ
⟹ (sin θ + 1)2 = (3 cos θ)2
⟹ (sin θ + 1)2 = 9 cos2 θ
⟹ (sin θ + 1)2 = 9(1 - sin2 θ)
⟹ sin2 θ + 2 sin θ + 1 = 9 – 9 sin2 θ
⟹ 10 sin2 θ + 2 sin θ – 8 = 0
⟹ 5 sin2 θ + sin θ – 4 = 0
⟹ 5 sin2 θ + 5 sin θ - 4 sin θ – 4 = 0
⟹ 5 sin θ (sin θ + 1) - 4 (sin θ + 1) = 0
⟹ (sin θ + 1) (5 sin θ – 4) = 0
Answers on Worksheet on finding the unknown angle using trigonometric identities are given below to check the exact answers of the questions.
Answers
1. 60°
2. 30°
3. 30°
4. 60°
5. 60°
6. γ°, where tan γ° = ½ or 2.
7. (i) No; 60°
(ii) No; 45°
8. 30°
9. 30°
From Worksheet on Finding the Unknown Angle Using Trigonometric Identities to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Oct 10, 24 05:15 PM
Oct 10, 24 10:06 AM
Oct 10, 24 03:19 AM
Oct 09, 24 05:16 PM
Oct 08, 24 10:53 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.