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In worksheet on establishing identities and simplification using trigonometric ratios of complementary angles we will solve various types of practice questions on trigonometric ratios of complementary angles. Here you will get 17 different types of questions on establishing identities and simplification using trigonometric ratios of complementary angles.
1. Prove that sin (90° - θ) sec θ + cos (90° - θ) csc θ = 2
2. Prove that sin θ cos (90° - θ) + cos θ sin (90° - θ) = 1
3. Prove that cos A cos (90° - A) - sin A sin (90° - A) = 0
4. Prove that cosθsin(90°−θ) + sinθcos(90°−θ) = 2
5. Prove that (1 + tan2 θ) cos θ cos (90° - θ) = cot (90° - θ)
6. Prove that cotθtan(90°−θ) + cos(90°−θ)tanθsec(90°−θ)sin(90°−θ)cot(90°−θ)csc(90°−θ) = 2
7. Prove that sinθsin(90°−θ) + cosθcos(90°−θ) = sec θ csc θ
8. Simplify: sin20°sin70° + cosθsin(90°−θ)
9. Simplify: cos70°sin20° + cos59°sin31° - 8 cos2 60°
10. Simplify: cos220°+cos270°sin259°+sin231° + sin 35° sec 55°
11. Simplify: sin80°cos10° + cos 59° csc 31°
12. Simplify: tan(90°−θ)cotθsec(90°−θ)cscθ
13. Simplify: sin2 A – cos2 B + sin2 (90° - A) – cos2 (90° - B)
14. If A + B = 90°, sin A= a and sin B = b then prove that a2 + b2 = 1.
15. In ∆ABC, prove that cos B+C2 = sin A2
16. In ∆ABC, prove that tan A+B2 = cot C2
17. In ∆ABC, prove that sec C+A2 = csc B2
Answers on Worksheet on Establishing Identities and Simplification Using Trigonometric Ratios of Complementary Angles are given below to check the exact answers of the questions.
Answers:
8. 2
9. 0
10. 2
11. 2
12. cos2 θ
13. 0.
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