SOLUTION: Hello Tutor, I really need your help to answer this question please. 3. Verify the following identity by using an angle sum identity: cos (2x) = 1 – 2(sin2 x). Hint (2x = x +

Algebra ->  Trigonometry-basics -> SOLUTION: Hello Tutor, I really need your help to answer this question please. 3. Verify the following identity by using an angle sum identity: cos (2x) = 1 – 2(sin2 x). Hint (2x = x +      Log On


   



Question 971855: Hello Tutor, I really need your help to answer this question please.
3. Verify the following identity by using an angle sum identity: cos (2x) = 1 – 2(sin2 x). Hint (2x = x + x)

Found 2 solutions by Boreal, anand429:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
double angle identity for cos (x+y)
=cosx*cosy - sinx*siny
=cosx^2 - sinx^2 since y=x
But cos^2 x + sin^2 x =1
Therefore, cos (2x)= 1-sin^2 x -sin^2 x substituting in two lines above.
cos (2x)=1-2 sin^2 x

Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
cos(2x) = cos(x+x)
=cosx*cosx -sinx*sinx
=%28cos%5E2%28x%29-sin%5E2%28x%29%29
=1-sin%5E2%28x%29-sin%5E2%28x%29
=1-2sin%5E2%28x%29