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Question

tan10tan15tan75tan80=?
(a) 3
(b) 13
(c) 1
(d) 1

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Solution

The correct option is (d): 1

We have:

tan10tan15tan75tan80

=tan10×tan15×tan(9015)×tan(9010)

=tan10×tan15×cot15×cot10 [tan(90θ)=cotθ]

=tan10×cot10×tan15×cot15

=1 [tanθ×cotθ=1]


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