Hi! Everyone, My name is Shivani. You probably know me, but if you don't I sit right in middle of Harsimran and Ruthanne. Now I shall introduce you with Solving Trigonometric Equations using Identities.


Trignometric Identities are equations involving the trignometric function that are true for every values of the variables involved. Youn can use trignometric identites along with algebric methods to solve trignometric equations.

Example
Find all the solutions of the equation in the interval 2sin²x=2+cosx

The equation contains both sine and cosine functions.
We rewrite the equation so that it contains only cosine functions using the Pythagorean Identity sin²x=1cos²x

Factoring cosx, we get,cosx(2cosx+1)=0

By using zero-product-property,we will get cosx=0,and 2cosx+1=0 whcih yields x= ^-1⁄₂
In the interval [0, 2π), we know that cosx=0 when x=^π⁄₂ and x= ^3π⁄₂ .On the other hand, we also know that cosx= ^-1⁄₂ when x= ^2π⁄₃ and x= ^4π⁄₃
Therefore, the solutions of the given equation in the interval [0, 2π) are { ^π⁄₂,^3π⁄₂,^2π⁄₃,^4π⁄₃}

I hope you've learned something ! And
Good luck for the test. :)