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Question

The value of tan 48.tan 23.tan 42.tan 67
and
cos 38.cos 52sin 38.sin 52 is equal to

A
1 and 0 respectively
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B
1 and 1 respectively
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C
1 and 2 respectively
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D
2 and 1 respectively
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Solution

The correct option is A 1 and 0 respectively
i) tan48.tan23.tan42.tan67

We know that, cot(90θ)=tanθ

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

We also know that, tanθ×cotθ=1

tan48.tan23.cot48.cot23
= tan48.cot48.tan23.cot23
= 1×1
= 1

ii) cos38.cos52sin38.sin52

We know that, cosθ=sin(90θ) and cosθ=sin(90θ)

cos38.cos52sin38.sin52
= cos38.sin(9052)sin38.cos(9052
= cos38.sin38sin38.cos38
= 0

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