Question

HELP AWARDING METAL!!

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x

Answer 1

soooo

\(\bf sin(x)\left[ tan(x)cos(x)-cot(x)cos(x) \right]=1-2cos^2(x)
\\ \quad \\ \quad \\
sin(x)\left[ {\color{brown}{ \cfrac{sin(x)}{\cancel{cos(x)}} }} \cancel{cos(x)}-{\color{brown}{ \cfrac{cos(x)}{sin(x)}}} cos(x) \right]
\\ \quad \\
sin(x)\left[ sin(x)-\cfrac{cos^2(x)}{sin(x)} \right]\implies sin(x)sin(x)-\cancel{sin(x)}\cfrac{cos^2(x)}{\cancel{sin(x)}}\)

what would you end up with there?