# How do you solve sin^2 = 2cosx - 2 algebraically?

##### 1 Answer

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#### Explanation

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**I am assuming the question is :**

We know the trigonometric identity

Subtract

Put this value of

Add

Now subtract

Now we have a quadratic equation in

We solve it by factorisation method (splitting the middle term) :

This gives us two solutions :

#cosx=-3# **(rejected)**, because#color(blue)(cosx in [-1,+1]# .#cosx= 1# **(accepted)**

The second one is the solution ,

**Moreover you can solve it graphically also**

Here are the curves of

**Note :** The colors of the graphs have been mentioned.

**Fun Fact :** Here

curves wherever they touch , i.e

For further references , read this : solving trigonometric equations

Hope it helps

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