Question

Trigonometric identity Prove Sin(8x)=2sin(4x)cos(4x)

Answer 1

$\bold{Answer}$

$\boxed{\bold{\Rightarrow \ \mathrm{True}}}$

$\bold{Explanation}$

• $\bold{Prove: \ \sin \left(8x\right)=2\sin \left(4x\right)\cos \left(4x\right)}$

$\bold{------------------}$

• $\bold{Manipulating \ Left \ Side: \ \sin \left(8x\right)}$

$\bold{\sin \left(2\cdot \:4x\right)}$

• $\bold{Use \ The \ Following \ Identity: \ \sin \left(2x\right)=2\cos \left(x\right)\sin \left(x\right)}$

$\bold{2\cos \left(4x\right)\sin \left(4x\right)}$

• $\bold{Two \ Sides \ Can \ Take \ The \ Same \ Form}$

$\bold{\Rightarrow \ \mathrm{True}}$

$\boxed{\bold{Eclipsed}}$