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Without using trigonometric tables, prove that: (i) sin 53∘ cos 37∘+cos 53∘ sin 37∘=1 (ii) cos 54∘ cos 36∘−sin 54∘ sin 36∘=0 (iii) sec 70∘ sin 20∘+cos 20∘ cosec 70∘=2 (iv) sin 35∘ sin 55∘−cos 35∘ cos 55∘=0 (v) (sin 72∘+cos 18∘)(sin 72∘−cos 18∘)=0 (vi) tan 48∘ tan 23∘ tan 42∘ tan 67∘=1 |
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Answer» Without using trigonometric tables, prove that: (i) sin 53∘ cos 37∘+cos 53∘ sin 37∘=1 (ii) cos 54∘ cos 36∘−sin 54∘ sin 36∘=0 (iii) sec 70∘ sin 20∘+cos 20∘ cosec 70∘=2 (iv) sin 35∘ sin 55∘−cos 35∘ cos 55∘=0 (v) (sin 72∘+cos 18∘)(sin 72∘−cos 18∘)=0 (vi) tan 48∘ tan 23∘ tan 42∘ tan 67∘=1 |
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