Please help with proving trig identities?

Question

1. sec(theta)sin(theta) over tan (theta) = 0
2. tan(theta){cot(theta)-cos(theta)} = 1 - sin(theta)
3. tan^2(theta) - 3 sin(theta)tan(theta)sec(theta) = -2tan^2(theta)
4. tan (pie - theta) = -tan(theta)
5. csc x(sin^2x + cos^2x tan x) over sin x +cos x = 1
6. cos(theta) - cos(theta)sin^2(theta) = cos^3(theta)

Answer 1

1) You meant to have a minus sign not "over". I've used x in place of "theta"
secx = 1/cosx and tanx = sinx/cosx
So 1 becomes (1/cosx)*sinx - tanx = 0
or tanx - tanx = 0, which is true.

2) tanx = 1/cotx, so tanx*cotx = 1
So 2 becomes 1- tanx*cosx = 1-sinx
But tanx = sinx/cosx so we have:
1- (sinx/cosx)*cosx = 1-sinx, so
1-sinx =1-sinx, which is true.

I'll do one more:

3) tan^2 x - 3sinx*tanx*secx = - 2tan^2 x
Again secx = 1/cosx and tanx = sinx/cosx
So 3. becomes:
tan^2 x - 3(sinx/cosx)*tanx = - 2tan^2 x, so
tan^2 x - 3tan^2 x = -2tan^2 x, so
tan^2 x = tan^2 x, which is true.

You need to learn to do these yourself: Here is a link which gives you all the trig identities to solve the rest. They are not difficult.

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Answer 2

1

Answer 3

SUGGESTIONS FOR PROVING IDENTITIES

(1)Do not assume LHS=RHS eg. by cross multiplying

(2)Using the basic identities, simplify the more complicated expression OR

(3)Rewrite both expressions in terms of Sine and Cosine

(4)Avoid taking square roots or raising to powers if possible.

(5)Note any restrictions on the variable

(6)Difference of two squares very useful in factoring

Answer 4

For number 1,
(sec Θ sin Θ)/tan Θ = (1/cos Θ)(sin Θ)/tan Θ = (tan Θ)/(tan Θ) = 1, not 0, as long as tan Θ is not 0.

So there's a problem here.