Worksheet on Establishing Equality using Trigonometric Ratios of Complementary Angles

In worksheet on establishing equality using trigonometric ratios of complementary angles we will solve various types of practice questions on trigonometric ratios of complementary angles. Here you will get 14 different types of questions on establishing equality using trigonometric ratios of complementary angles.

1. If θ and β are two complementary angles, prove that

(i) sin2 θ + sin2 β = 1

(ii) cot β + cos β = \(\frac{cos β}{cos θ}\) (1 + sin β)

(iii) \(\frac{sec θ}{cos θ}\) - cot2 β = 1

2. Prove that sin 40° + sin 75° = cos 15° + cos 50°


3. Prove that cos 1° - cos 89° = sin 89° - sin 1°


4. Prove that sin 18° + cos 67° = sin 23° + cos 72°


5. Prove that tan 62° - cot 48° = cot 28° - tan 42°


6. Show that sec2 12° - \(\frac{1}{tan^2 78°}\) = 1


7. Prove that tan 15° tan 30° tan 45° tan 60° tan 75° = 1


8. Prove that cot 9° cot 27° cot 45° cot 63° cot 81° = 1


9. csc2 22° ∙  cot 68° = sin2 22° + sin2 68° + cot2 68°


10. Prove that cos2 1° + sin2 23° + sin2 67° + cos2 89° = 2


11. Prove that sin2 85° + sin2 80° + sin2 10° + sin2 5° = 2


12. Prove that sec 44° csc 46° - tan 414° cot 46° = 1

13. If sin 17° = \(\frac{x}{y}\), show that, sec 17° - sin 73° = \(\frac{x^{2}}{y\sqrt{y^{2} - x^{2}}}\)


14. Prove that \((\frac{sin 47°}{cos 43°})^{2}\) + \((\frac{cos 43°}{sin 47°})^{2}\) - 4 cos2 45° = 0.

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