# Trigonometry

posted by .

Find the exact value of tan(a-b)

sin a = 4/5, -3pi/2<a<-pi;
tan b = -sqrt2, pi/2<b<pi

identity used is:

tan(a-b)=(tan a-tan b)/1+tan a tan b

(a is alpha, b is beta)

• Trigonometry -

Both the sine and cosine curves are the same for
-3pi/2<a<-pi as they are for π/2<a<π (2nd quad)
so if sina = 4/5, then cosa = -3/5
and tana = -4/3

then tan(a-b)
= (tana - tanb)/(1 + tanatanb)
= ((-4/3) - (-√2))/( 1 + (-4/3)(-√2))
= (√2 - 4/3)/(1 + 4√2/3)
= (3√2 - 4)/(3 + 4√2)

I don't know if you have to rationalize that, if you do carefully multiply top and bottom by (3 - 4√2)

• Trigonometry -

I put that in but it said the answer was
36-25ã2/23
any idea how that works?

• Trigonometry -

That is exactly what my answer works out to if you rationalize it.
I had suggested to do that.

• Trigonometry -

8 cot(A) − 8/
1 + tan(−A)

## Similar Questions

1. ### Integration

Intergrate ¡ì sec^3(x) dx could anybody please check this answer. are the steps correct?
2. ### 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 …
3. ### calculus

can anyone tell me if tan-1x= 1 over tan x?
4. ### 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 …
5. ### Trig - tan 15° using composite argument?

tan 15° tan (45°-30°) (tan 45° - tan 30°)/1+ tan 45°tan30° (1-√3/3)/(1+1√3/3) then i donnt what to do/ chancel out. Can someone finish it if i didn't get it wrong. thanks in advance
6. ### Maths Calculus Derivatives

Find the first derivative for the following functions 1) f(x) = sin(cos^2x) cos(sin^3x) 2) f(x) = ( tan 2x - tan x ) / ( 1 + tan x tan 2x ) 3) f(x) = sin { tan ( sqrt x^3 + 6 ) } 4) f(x) = {sec^2(100x) - tan^2(100x)} / x
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 desperate help, clueless girl here

2. solve cos 2x-3sin x cos 2x=0 for the principal values to two decimal places. 3. solve tan^2 + tan x-1= 0 for the principal values to two decimal places. 4. Prove that tan^2(x) -1 + cos^2(x) = tan^2(x) sin^2 (x). 5.Prove that tan(x) …
10. ### Math-Trigonometry

Show that if A, B, and C are the angles of an acute triangle, then tan A + tan B + tan C = tan A tan B tan C. I tried drawing perpendiculars and stuff but it doesn't seem to work?

More Similar Questions