prove that tan10°.tan25°.tan45°tan65°tan80°=1
Answers
Answer:
Answer:
L.H.S. = tan 10˚ tan 15˚ tan 75˚ tan 80˚
= tan 10˚ tan 15˚ tan (90˚ – 15˚) tan(90˚ – 10˚)
= tan 10˚ tan 15˚ cot 15˚ cot 10˚
1/cot10˚ × 1/cot 15˚ × cot 15˚ × cot 10˚
= 1 = R.H.S.
Hence proved.
(ii) L.H.S. = cos 1˚ cos 2˚ cos 3˚ …..cos 180˚
= cos1˚ cos2˚ cos 3˚ …..cos 89˚ cos 90˚ ….cos 180˚
= cos 1˚ cos 2˚ cos 3˚ ….cos 89˚ × 0 × cos 91˚ ….cos 180˚
= 0 = R.H.S.
Hence proved.
Step-by-step explanation:
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Step-by-step explanation:
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Answer:
L.H.S. = tan 10˚ tan 15˚ tan 75˚ tan 80˚
= tan 10˚ tan 15˚ tan (90˚ – 15˚) tan(90˚ – 10˚)
= tan 10˚ tan 15˚ cot 15˚ cot 10˚
1/cot10˚ × 1/cot 15˚ × cot 15˚ × cot 10˚
= 1 = R.H.S.
Hence proved.
(ii) L.H.S. = cos 1˚ cos 2˚ cos 3˚ …..cos 180˚
= cos1˚ cos2˚ cos 3˚ …..cos 89˚ cos 90˚ ….cos 180˚
= cos 1˚ cos 2˚ cos 3˚ ….cos 89˚ × 0 × cos 91˚ ….cos 180˚
= 0 = R.H.S.
Hence proved.