Question

Verify that the equation is an identity ;
the following ......

Answer 1

\[\cos \left( x -\frac{ \pi }{ 6 }\right)+\sin \left( x-\frac{ \pi }{ 3 } \right)=sinx\]

Answer 2

you use the difference identities for sin and cos

Answer 3

I did used them , but then I didn't know how to complete ?

Answer 4

\[\cos(x)\cos(\frac{\pi}{6})+\sin(x)\sin(\frac{\pi}{6})+\sin(x)\cos(\frac{\pi}{3})-\sin(\frac{\pi}{3})\cos(x) \\ \cos(x) \frac{\sqrt{3}}{2}+\sin(x)\frac{1}{2}+\sin(x)\frac{1}{2}-\frac{\sqrt{3}}{2}\cos(x)\]
combine like terms

Answer 5

thank you