Math

How do I solve this?
tan^2x= 2tanxsinx

My work so far:
tan^2x - 2tanxsinx=0
tanx(tanx - 2sinx)=0

Then the solutions are:

TanX=0

and
sinX/cosX = 2 sin X

Divide through by sinX: we have to check this later to see if allowed (ie sinX is not zero)
cosX=1/2
Now, if CosX=1/2, then sinX must equal sqrt3/2, from cos^2 + sin^2=1 for any angle.

So, solutions: x = arctan 0
and x=arccos 1/2

check that.

  1. 👍 0
  2. 👎 0
  3. 👁 1,052

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Find the limit lim as x approaches (pi/2) e^(tanx) I have the answer to be zero: t = tanx lim as t approaches negative infi e^t = 0 Why is tan (pi/2) approaching negative infinity is my question?

  2. TRIGONOMETRY *(MATHS)

    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.

  3. arithmetic

    if tanx+cotx=2 then the value of tan^5x + cot^10x is

  4. Trig-Weird Geometry Problem

    Determine all triangles ABC for which tan(A-B)+tan(B-C)+tan(C-A)=0. There's a hint: "Can you relate A-B to B-C and C-A?" Should I apply the tangent difference formula (tan(x-y))? Help would be appreciated, thanks.

  1. Maths

    How do I prove that 7sin^2x - sinxcosx = 6 can also be written as tan^2x + tanx - 6 = 0 ?

  2. Maths

    tanx = -3/4. x€ 2nd quadrant find sin (x/2), cos(x/2), tan(x/2)

  3. trigonometry

    Given tanx=8/15 when pi < x < 3pi/2, find tan x/2.

  4. trignometry

    tanx+cotx=5 than find the value of tan^2x+cot^2x

  1. solving trig. equations

    tan(3x) + 1 = sec(3x) Thanks, pretend 3x equals x so tanx + 1 = secx we know the law that 1 + tanx = secx so tanx + 1 becomes secx and... secx = secx sec(3x) = sec(3x) [just put 3x back in for x- you don't really have to change 3x

  2. Trigonometry

    Hello, everyone: I am working on finding the exact values of angles that are less common and are therefor not found easily on the Unit Circle (at least, they are not labeled). For example, the problem I am asking about is: 10)

  3. Trigonometry

    How do I solve these? 1) 2sinxcosx-cosx=0 2) cos^2(x)-0.5cosx=0 3) 6sin^2(x)-5sinx+1=0 4) tan^2(x)+tanx-12=0

  4. trig

    simplify the expression. tan(π/2-x)tanx

You can view more similar questions or ask a new question.