sin(60+x)-sin(60-x)=1 the interval 0<x<2pi how do you solve?

1 Answer
Feb 17, 2018

x=pi/2

Explanation:

We want to solve the equation

sin(60^@+x)-sin(60^@-x)=1

We will use the identity

  • sin(a+b)-sin(a-b)=2sin(b)cos(a)

(Can be derived using angle-sum and difference identities)

/

Apply the identity (a=60 and b=x)

2sin(x)cos(60^@)=1

Solve for sine

sin(x)=1/(2cos(60^@))

=1/(2*1/2)

=1

By the inverse sine

x=pi/2