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Complementary Trigonometric Ratios

Prove thattan...

Question

Prove that
tan10 tan15 tan75 tan80=1

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Solution

Tan10 tan15 tan(90-75) tan (90-80)
= tan10 tan15 cot 15 cot10
as we know tan theta * cot theta = 1
so
tan10 cot10 tan15 cot 15
= 1

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