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23 December, 10:55

Using sums and differences, calculate:

a) cos 15

b) cotg 165

c) cossec 15

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Answers (1)
  1. 23 December, 14:09
    0
    in steps

    Step-by-step explanation:

    cos 15° = cos (45° - 30°) = cos 45° cos 30° + sin 45° sin 30°

    = (√2 / 2) (√3 / 2) + (√2 / 2) (1 / 2)

    = (√3/2√2) + (1/2√2)

    = (√3 + 1) / 2√2 (0.9659)

    cot 165° = cot (90° + 75°) = - tan 75° = - (2 + √3)

    csc 15° = 1 / sin 15° = 1 / sin (45° - 30°)

    = 1 / (sin 45° cos 30° - cos 45° sin 30°)

    = 1 / (√2/2 x √3/2 - √2/2 x 1/2)

    = 1 / ((√6 - √2) / 4)

    = 4 / (√6 - √2)

    =√6 + √2
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