Question

Please help, But explain. FLVS isn't very good at explaining - so now I'm asking you guys!! Thanks so much :3
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

1: cot x sec^4x = cot x + 2 tan x + tan^3x
2: (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos^2x
3: 1 + sec^2x sin^2x = sec^2x
4: sine of x divided by one minus cosine of x + sine of x divided by one minus cosine of x = 2 csc x
5: - tan^2x + sec^2x = 1

Answer 1

I am your algebra teacher from FLVS

Answer 2

@Compassionate @Michele_Laino @sleepyjess

Answer 3

for #1

\(\cot x\sec^4x \\~\\=\cot x (\sec^2x)^2\\~\\=\cot x(1+\tan^2x)^2\)


next try using below identity
\[(a+b)^2=a^2+2ab+b^2\]