# If #sqrt(sinx) + cosx = 0#, the what is the value of #sinx#?

##### 3 Answers

#### Explanation:

**Squaring,**

**Completing Square** on the **L.H.S.,** we find,

But because of **not admissible.**

See below.....

#### Explanation:

#sqrt(sinx)+cosx=0#

#=>sqrtsinx=-cosx#

#=>sinx=cos^2x#

#=>sinx=1-sin^2x#

#=>sin^2x+sinx-1=0#

#=>m^2+m-1=0" "" where"" " m=sinx#

Now,

Solution of

This is the answer for

#sinx=(sqrt5-1)/2# as#-1 < sinx < +1#

Graphical representation:-

graph{x^2+x-1 [-7.83, 12.17, -4.81, 5.19]}

We have to manipulate the equation to a more manageable form, and then solve it.

#### Explanation:

If

So we have

Now this is a quadratic equation in

We get two solutions:

But now, we should observe that

Note 1: We have to be careful not to introduce false solutions. Say we have

Note 2: The solution