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Introduction to Trigonometry
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13/06/2021 11:39 am
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Show that:
(i) tan 48° tan 23° tan 42° tan 67° = 1
(ii) cos 38° cos 52° – sin 38° sin 52° = 0
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13/06/2021 11:41 am
(i) tan 48° tan 23° tan 42° tan 67°
We know that, tan 48° = tan (90° – 42°) = cot 42°
tan 23° = tan (90° – 67°) = cot 67°
= tan (90° – 42°) tan (90° – 67°) tan 42° tan 67°
Substitute the values
= cot 42° cot 67° tan 42° tan 67°
= (cot 42° tan 42°) (cot 67° tan 67°) = 1×1 = 1
(ii) cos 38° cos 52° – sin 38° sin 52°
We know that,
cos 38° = cos (90° – 52°) = sin 52°
cos 52°= cos (90°-38°) = sin 38°
= cos (90° – 52°) cos (90°-38°) – sin 38° sin 52°
Substitute the values
= sin 52° sin 38° – sin 38° sin 52° = 0