Question

96 points here, having to ask same question again - please help a brother out.

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

1. cot x sec^4 x = cot x + 2 tan x + tan^3 x
2. (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos^2 x
3. 1 + sec^2 x sin^2 x = sec^2 x
4. ((sin x)/(1-cos x)) + ((sin x)/(1+cos x))=2csc x
5. - tan^2 x + sec^2x = 1

Answer 1

the equation is - tan2 x + sec2 x = 1.

Left hand side identity : - tan2 x + sec2 x.

Trigonometric function : tan x = sin x / cos x,

Reciprocal identity : sec x = 1/cos x.

- tan2 x + sec2 x = - (sin x/cos x)2 + (1/cos x)2

= - sin2 x/cos2 x + 1/cos2 x

= (1 - sin2 x)/cos2 x

Pythagorean identity : sin2 x + cos2 x = 1 .

= cos2 x / cos2 x

= 1

Answer 2

see attached pictures for answers