I need help with verifying identities?

Question

0 is the zero with the line through it
Verify this identity sin 0 cot 0 = cos 0
Simplify this trignometric expression 1-cos^2 0
And simplify this trig expression csc 0 cos 0 tan 0

Answer 1

The best advice I have is rewrite all the trig functions in terms of just sine and cosine. that should work on the first and third ones. The second one... well, I'm not sure what is meant by "simplify" - there's a lot of different ways to go here. But one thought is that it is a difference of squares - but most likely you just need to take a look at the pythagorean identies for a hint.

I hope this is enough help to get you going - Good luck!

Answer 2

3.trignometric expression 1-cos^2 0=sin^2(theta). answer

Answer 3

Theta is the zero with the line through it.


sin theta cot theta = cos theta.

sin theta (cos theta/sin theta) = cos theta.

cos theta = cos theta.


sin^2 theta + cos^2 theta = 1^2

{sin^2 theta} = 1 - cos^2 theta



csc theta cos theta tan theta =
(1/sin theta)(cos theta)(sin theta/cos theta) =
1.

Answer 4

I am going to use a instead of theta. It's easier to see.
sin(a)cot(a)

cot(a) = 1/tan(a)
so sin(a)/tan(a)

tan(a) = sin(a)/cos(a)
so sin(a)/ (sin(a)/cos(a))
or sin(a) * cos(a)/sin(a)
= cos(a)

1-cos^2(a)
cos^2(a) + sin^2(a) = 1 (from pythagorus)
1 - cos^2(a) = sin^2(a)

csc(a)* cos(a)* tan(a)
csc(a) = 1/sin(a)
tan(a) = sin(a)/cos(a)

(1/sin(a))* cos(a)* sin(a)/cos(a) = 1

Answer 5

cot= cos/sin
so sin0*cos0 /sin0= cos 0 (sine's cancel out)

cos^2(0)+sin^2(0)=1
so 1-cos^2(0)
=[cos^2(0)+sin^2(0)]-cos^2(0)
= sin^2(0)

csc 0 cos 0 tan 0= (1/cos 0 ) (cos 0) (sin0/cos0)= (sin0/cos0)= tan 0

Answer 6

Let angle be x
Question 1
sin x . cot x = sin x. cos x / sin x = cos x

Question 2
1 - cos ² x = sin ² x

Question 3
cosec x.cos x.tan x
= (1 / sin x).(cos x).(sin x / cos x)
= 1

Answer 7

tan²θ - sin²θ = sin²θ/cos²θ - sin²θ = sin²θ(1/cos²θ - 1) = sin²θ(1 - cos²θ)/cos²θ = sin²θ * sin²θ/cos²θ = sin²θ * tan²θ I know someone else already answered, but he used faulty logic. He assumed from the get-go that the result was true, and showed no contradiction, which doesn't actually prove the result.