Verify cos x(cot x + tan x) = csc x

Question

Verify the equation to see if one side would equal the other.

Answer 1

kosine*tan=kosine*(sine/kosine)=sine...sine^2/sine

kosine*kotan=kosine*(kosine/sine)=kosine^2/sine

sum=(sine^2 +kosine^2)/sine=1/sine...kosekant

Answer 2

Prove that,

cos(x)(cot(x)+tan(x)) = csc(x) = 1/sin(x)

manipulate the lhs

cos(x){cos(x)/sin(x) + sin(x)/cos(x)}

cos(x){cos^2(x)/[cos(x)sin(x)] + sin^2(x)/[cos(x)sin(x)]}

cos(x){cos^2(x) + sin^2(x)}/[cos(x)sin(x)]

cos(x){1}/[cos(x)sin(x)]

1/sin(x) = rhs

Q.E.D.