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Introduction to Trigonometry
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16/06/2021 10:49 am
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Evaluate:
(i) \(\frac{sin^2 63° + sin^2 27°}{cos^2 17° + cos^2 73°}\)
(ii) sin 25° cos 65° + cos 25° sin 65°
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16/06/2021 10:54 am
(i) \(\frac{sin^2 63° + sin^2 27°}{cos^2 17° + cos^2 73°}\)
= \(\frac{sin^2 (90°-27°) + sin^2 27°}{cos^2 (90°-73°) + cos^2 73°}\)
= \(\frac{sin^2 27° + sin^2 27°}{cos^2 27° + cos^2 73°}\)
= 1/1 = 1 (since sin2A + cos2A = 1)
Therefore, \(\frac{sin^2 63° + sin^2 27°}{cos^2 17° + cos^2 73°}\) = 1
(ii) sin 25° cos 65° + cos 25° sin 65°
= sin(90°-25°) cos 65° + cos (90°-65°) sin 65°
= cos 65° cos 65° + sin 65° sin 65°
= cos265° + sin265° = 1 (since sin2A + cos2A = 1)
Therefore, sin 25° cos 65° + cos 25° sin 65° = 1