# Finding a formulai need to find the formula of sin 3x

justaguide | Certified Educator

The formula of sin 3x can be determined from the basic formula for the cos of the sum of two angles a and b and the sine of the sum of two angles.

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

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

cos 3x = cos (2x + x) = cos 2x * cos x - sin 2x *sin x

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

=> [cos x * cos x - sin x * sin x] * cos x - [ sin x*cos x + cos x*sin x]*sin x

=> (cos x)^3 - 3*(sin x)^2 *cos x

=> (cos x)^3 - 3*[1 - (cos x)^2] *cos x

=> (cos x)^3 - 3*cos x + 3*(cos x)^3

=> 4*(cos x)^2 - 3*cos x

cos 3x = 4*(cos x)^2 - 3*cos x
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