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Rajan@2021
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Without using trigonometric tables, prove that: (sin72° + Cos18°)(sin72° – cos18°) = 0

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This question is from trigonometry

Topic – trigonometric ratios on complementary angles

We have been asked to prove that (sin72° + cos18°)(sin72° – cos18°)= 0

without using trigonometric tables

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

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  1. LHS = (sin72° + cos18°)(sin72° − cos18°)

    =(sin²72° – cos²18°)

    = (sin²72° – cos²(90° – 72°))

    = sin²72° – sin²72°

    = 0 = RHS

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