Question

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

Answer 1

`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`