Prove that: tan10 tan 15 tan75 tan80 =1
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Answered by
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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.
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Step-by-step explanation:
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.
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