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Rajan@2021
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Without using trigonometric tables, prove that: tan48°tan23°tan42°tan67° = 1

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This question is from trigonometry

Topic – trigonometric ratios on complementary angles

We have to prove that tan48°tan23°tan42°tan67° = 1

RS Aggarwal, Class 10, chapter 12, question no 3(vi).

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  1. tan 48° tan 23° tan 42° tan 67°

    = tan (90° – 42°) tan (90° – 67°) tan 42° tan 67°

    = cot 42° cot 67° tan 42° tan 67°

    = (cot 42° tan 42°) (cot 67° tan 67°)

    = 1×1

    = 1

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