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Question

Please if you can help me find the answer to this.

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.

cos(13𝜋/15)cos(-𝜋/5)-sin(13𝜋/15)sin(-𝜋/5)

Answer 1

cos(13𝜋/15)cos(-𝜋/5)-sin(13𝜋/15)sin(-𝜋/5) = cos(13π/15 - π/5) = cos(10π/15) = cos(2π/3) = - 1/2

Answer 2

cos(13𝜋/15)cos(-𝜋/5)-sin(13𝜋/15)sin(-𝜋/5)

This has the format of a trig identity - Cos (A+B) = Cos A Cos B - SinA SinB

Then = Cos ( 13π/15 + (-π/5) )

= Cos( 12π/5) = Cos(144°) = -0.809