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Question

tan 48.tan 23.tan 42.tan 67 = ___

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Solution

We know that cot(90θ)=tanθ

tan48.tan23.tan42.tan67
= tan48.tan23.cot(9042).cot(9067)
= tan48.tan23.cot48.cot23

We also know that tanθ×cotθ=1

tan48.tan23.cot48.cot23
= tan48.cot48.tan23.cot23
= 1×1
= 1
Thus, tan48.tan23.tan42.tan67=1

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