How do I prove that sin (x + pi) = -sin x?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

To prove that sin(x + pi) = -sin x, use the expansion for sin(a + b).

sin(a + b) = sin a * cos b + cos a * sin b

sin(x + pi)

=> sin x * cos pi + cos x * sin pi

sin pi = 0 and cos pi = -1

=> sin x * (-1) + cos x * 0

=> - sin x

This proves that sin ( x + pi) = - sin x

lochana2500's profile pic

lochana2500 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

sin (x + π) = sinx.cosπ + cosx.sinπ

we know that sinπ=0 and cosπ= (-1)

= sinx.(-1) + cosx. 0

= -sinx + 0

= -sinx

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