# Trigonometry

posted by .

Prove that 1+tan(Theta)/1-tan(Theta) = sec^2(Theta)+2tan(Theta)/1-tan^2(Theta)

If you explain, that would be great (:

• Trigonometry -

(1+tan)/(1-tan)

multiply top and bottom by 1+tan

(1+tan)^2 / (1-tan)(1+tan)

(1 + 2tan + tan^2)/(1-tan^2)

now, since sec^2 = 1+tan^2,

(sec^2 + 2tan)/(1-tan^2)

## Similar Questions

1. ### Maths- complex numbers

Find tan(3 theta) in terms of tan theta Use the formula tan (a + b) = (tan a + tan b)/[1 - tan a tan b) in two steps. First, let a = b = theta and get a formula for tan (2 theta). tan (2 theta) = 2 tan theta/[(1 - tan theta)^2] Then …
2. ### I dont think drawing a picture will help me drwls

Which expression is equivalent to tan theta-sec theta/sin theta?
3. ### Calculus

I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure …
4. ### trig

h t t p : / / i m g 4 0 . i m a g e s h a c k . u s / c o n t e n t . p h p ?
5. ### calculus

I need to prove that the following equation is an identity: (1 + tan(theta/2))/(1-tan(theta/2))=tan(theta)+sec(theta)
6. ### trig

If sin theta is equal to 5/13 and theta is an angle in quadrant II find the value of cos theta, sec theta, tan theta, csc theta, cot theta.
7. ### math

I have a question I have been working on since yesterday and I am not making this up. I couldn't get the right answer. If sin theta = -2/3, which of the following are possible?
8. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …
9. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …
10. ### Precalculus

Circle O below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of theta. Your answer to this problem should be a six letter sequence whose letters represent the segment …

More Similar Questions