# Trig Identities

posted by .

Proving identities:

1) 1+ 1/tan^2x = 1/sin^2x

2) 2sin^2 x-1 = sin^2x - cos^2x

3) 1/cosx - cosx = sin x tan x

4) sin x + tan x =tan x (1+cos x)

5) 1/1-sin^2x= 1+tan^2 x

How in the world do I prove this...please help...

I appreciateyour time thankyou soo much!!

• Trig Identities -

There is on one correct and foolproof way to prove identities.
There are some general rules you might follow
1. look for obvious relations , like sin^2 x + cos^2 x = 1
or 1 + tan^2 x = sec^2 x
-- make yourself a summary of these collected from your text or notebooks
2. usually, changing all ratios to sines and cosines often gives quick and easy results
3. start with the more complicated looking side, and try to work it towards the expression on the other side , or
4. work down one side until you can't seem to go any further, now switch to the other side and try to obtain that last expression

e.g. #4
sinx + tanx = tanx (1+cosx)

LS = sinx + sinx/cosx
= (sinxcosx + sinx)/cosx
= sinx(cosx + 1)/cosx
= (sinx/cosx)(1 + cosx)
= tanx (1 + cosx)
= RS

#2
2sin^2 x - 1 = sin^2x - cos^2x

RS = sin^2 x - (1 - sin^2 x)
= sin^2 x - 1 + sin^2 x
= 2sin^2 x - 1
= LS
well, that was an easy one

try the others by using similar methods.
come back if you get stuck.

• small correction - Trig Identities -

My first line should have been:

There is NO one correct and foolproof way to prove identities.

• Trig Identities -

OHHH!!! Ok thankyou soooo much I greatly appreciate your help and one compliment...Your way better than my teacher...once again thankyou sooo much I think I get the jist of it now:)

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### Trig

Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
2. ### Trig.......

I need to prove that the following is true. Thanks (2tanx /1-tan^x)+(1/2cos^2x-1)= (cosx+sinx)/(cosx - sinx) and thanks ........... check your typing. I tried 30º, the two sides are not equal, they differ by 1 oh , thank you Mr Reiny …
3. ### Mathematics - Trigonometric Identities

Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y …
4. ### trig 26

simplify to a constant or trig func. 1. sec ²u-tan ²u/cos ²v+sin ²v change expression to only sines and cosines. then to a basic trig function. 2. sin(theta) - tan(theta)*cos(theta)+ cos(pi/2 - theta) 3. (sec y - tan y)(sec y + …
5. ### Trigonometry

Please review and tell me if i did something wrong. Find the following functions correct to five decimal places: a. sin 22degrees 43' b. cos 44degrees 56' c. sin 49degrees 17' d. tan 11degrees 37' e. sin 79degrees 23'30' f. cot 19degrees …
6. ### TRIG..............

Q.1 Prove the following identities:- (i) tan^3x/1+tan^2x + cot^3x/1+cot^2 = 1-2sin^x cos^x/sinx cosx (ii) (1+cotx+tanx)(sinx-cosx)/sec^3x-cosec^3x = sin^2xcos^2x.
7. ### Trigonometry

1.Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two decimal places. 6.Prove that tan y cos^2 y + sin^2y/sin y = cos y + sin y 10.Prove that 1+tanθ/1-tanθ = sec^2θ+2tanθ/1-tan^2θ 17.Prove that …
8. ### precalculus

For each of the following determine whether or not it is an identity and prove your result. a. cos(x)sec(x)-sin^2(x)=cos^2(x) b. tan(x+(pi/4))= (tan(x)+1)/(1-tan(x)) c. (cos(x+y))/(cos(x-y))= (1-tan(x)tan(y))/(1+tan(x)tan(y)) d. (tan(x)+sin(x))/(1+cos(x))=tan(x) …
9. ### Trigonometry

Prove the following trigonometric identities. please give a detailed answer because I don't understand this at all. a. sin(x)tan(x)=cos(x)/cot^2 (x) b. (1+tanx)^2=sec^2 (x)+2tan(x) c. 1/sin(x) + 1/cos(x) = (cosx+sinx)(secx)(cscx) d. …
10. ### Trig Identities

Prove the following identities: 13. tan(x) + sec(x) = (cos(x)) / (1-sin(x)) *Sorry for any confusing parenthesis.* My work: I simplified the left side to a. ((sinx) / (cosx)) + (1 / cosx) , then b. (sinx + 1) / cosx = (cos(x)) / (1-sin(x)) …

More Similar Questions