Asked by Hope
Simplify to a single term
Sin(540-x).sin(-x) -cos(180-x).sin(90+x)
Sin(540-x).sin(-x) -cos(180-x).sin(90+x)
Answers
Answered by
mathhelper
Play with the identities
sin(540 - x) = sin(180 - x) = sinx , (540° is one rotation + 180°)
sin(-x) = sinx
cos(180-x) = -cosx
sin(90+x) = sin90cosx + cos90sinx = cosx + 0 = cosx
Sin(540-x).sin(-x) -cos(180-x).sin(90+x)
= (sinx)(sinx) - (-cosx)(cosx)
= sin^2 x + cos^2 x
= 1
sin(540 - x) = sin(180 - x) = sinx , (540° is one rotation + 180°)
sin(-x) = sinx
cos(180-x) = -cosx
sin(90+x) = sin90cosx + cos90sinx = cosx + 0 = cosx
Sin(540-x).sin(-x) -cos(180-x).sin(90+x)
= (sinx)(sinx) - (-cosx)(cosx)
= sin^2 x + cos^2 x
= 1
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