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Prove that: cos15° cos35° cosec55° cos60° cosec75° = 2

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This question is from trigonometry topic- trigonometric ratios on complementary angles in which we have been asked to prove that cos15° cos35° cosec55° cos60° cosec75° = 2

RS Aggarwal, Class 10, chapter 12, question no 6(iii)

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  1. Consider L.H.S. = cos 15° cos 35° cosec 55° cos 60° cosec 75°

    = cos 15° cosec 75° cos 35° cosec 55° cos 60°

     

    = cos 15° cosec (90-15)° cos 35° cosec (90-35)° cos 60°

     

    = (cos 15° sec 15°) × (cos 35° sec 35°) × cos 60°

     

    = (1) × (1) × (1/2)

     

    = 1/2 = R.H.S.

     

    Hence, proved.

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