# precal

posted by .

The values of x that are solutions to the equation cos^(2)x=sin2x in the interval [0, pi] are

a. arctan(1/2) only
b. arctan(1/2) and pi
c. arctan(1/2) and 0
d. arctan(1/2) and (pi/2)
e. arctan(1/2), o, and (pi/2)

• precal -

cos^2 x - sin 2x = 0 , 0 ≤ x ≤ π
cos^2 x - 2sinxcosx= 0
cosx(cosx - 2sinx) = 0
cosx = 0
x = π/2
or
cosx = 2sinx
cosx/sinx = 2
sinx/cosx = 1/2
tanx = 1/2 , tan is positive only in I for our domain
x = arctan(1/2)

so it looks like D

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### Calculus

Note that pi lim arctan(x ) = ---- x -> +oo 2 Now evaluate / pi \ lim |arctan(x ) - -----| x x -> +oo \ 2 / I'm not exactly sure how to attempt it. I have tried h'opital's rule but I don't believe you can use it here. Any help …
2. ### calculus

Let f be a function defined by f(x)= arctan x/2 + arctan x. the value of f'(0) is?
3. ### calc

also: integral of tan^(-1)y dy how is integration of parts used in that?
4. ### Trigonometry

I need help with I just can't seem to get anywhere. this is as far as I have got: Solve for b arcsin(b)+ 2arctan(b)=pi arcsin(b)=pi-2arctan(b) b=sin(pi-2arctan(b)) Sub in Sin difference identity let 2U=(2arctan(b)) sin(a-b)=sinacosb-cosasinb …
5. ### Math

Arrange these in order from least to greatest: arctan(-sqrt3), arctan 0, arctan(1/2) So far I got the first two values, arctan(-sqrt3), and that's 150 degrees. Arctan 0 would be zero degrees. I'll use just one answer for now, but I …
6. ### calculus

Now we prove Machin's formula using the tangent addition formula: tan(A+B)= tanA+tanB/1-tanAtanB. If A= arctan(120/119) and B= -arctan(1/239), how do you show that arctan(120/119)-arctan(1/239)=arctan1?
7. ### calculus

h(x)= integral from (1, 1/x) arctan(2t)dt part 1: let U= 1/x and du= ?
8. ### calculus

h(x)= integral from (1, 1/x) arctan(2t)dt part 1: let U= 1/x and du= ?
9. ### PRE-CALC

sin(arctan(-4/3) okay so i made arctan(-4/3) = x so im solving for sin(x) and x= arctan(-4/3) so then tanx = -4/3 and now im stuck i don't know what to do after that
10. ### check my arctan please

arctan(1/12)= 4.763 rounded to the nearest tenth degree, which is 4.8?

More Similar Questions