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29 August, 05:52

Find the exact value of sin - 255°.

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  1. 29 August, 07:24
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    sin (-255°) = √2 + √6/4

    Step-by-step explanation:

    We need to find sin - 255°

    We know that sin (-a) = - sin (a)

    so, sin (-255°) = - sin 255°

    We know that 180° + 75° = 255°

    Now we can write sin (255°) = sin (180° + 75°)

    We can use the identity:

    sin (x+y) = sin (x) cos (y) + cos (x) sin (y)

    x = 180°, y = 75°

    Solving,

    sin (x+y) = sin (x) cos (y) + cos (x) sin (y)

    sin (180° + 75°) = sin (180°) cos (75°) + cos (180°) sin (75°)

    sin (180°) = 0

    cos (75°) = √6 - √2/4

    cos (180°) = - 1

    sin (75°) = √2 + √6/4

    Putting values,

    sin (180° + 75°) = 0 (√6 - √2/4) + (-1) (√2 + √6/4)

    sin (180° + 75°) = - (√2 + √6/4)

    We know that sin (-255°) = - sin (255°)

    Putting value of sin (255°)

    sin (-255°) = - ( - (√2 + √6/4))

    sin (-255°) = √2 + √6/4
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