Wednesday, December 18, 2013

How to solve the equation `sqrt(3)sin x-cosx=0` ?

The question is not very clear, i.e is it sqrt(3)
sinx-cosx =0 or sqrt(3sinx)-cos x=0


I will do it for the
questions:


1) sqrt(3) sinx - cos x
=0


or sqrt (3) sinx = cos


or, sinx/cosx = tanx =
1/sqrt(3) 


i.e. x = pi/6 (or 30
degrees)


2) sqrt (3 sinx)-cosx=
0


or 3sinx = cos^2 x = 1- sin^2
x


(using sin^2 x + cos^2 x =
1)


or, sin^2x + 3 sinx -1 =
0


solving this quadratic equation, we get sin x = (1/2) x
(-3+ sqrt (13))


or, x = 17.62
degrees
.

No comments:

Post a Comment

Can (sec x - cosec x) / (tan x - cot x) be simplified further?

Given the expression ( sec x - csec x ) / (tan x - cot x) We need to simplify. We will use trigonometric identities ...