Question

Simplify (1 − sin x)(1 + sin x).

Answer 1

`(1-\sin x )(1+\sin x)=\cos^2x`

Explanation:

Given : Expression
`(1-\sin x )(1+\sin x)`

To find : Simplify the expression ?

Solution :

Step 1 - Write the expression,

`(1-\sin x )(1+\sin x)`

Step 2 - Applying identity,
`(a+b)(a-b)=a^2-b^2`

`(1-\sin x )(1+\sin x)=1^2-\sin^2x`

`(1-\sin x )(1+\sin x)=1-\sin^2x`

Step 3 - Applying trigonometric identity,
`\sin^2x+\cos^2x=1`

`(1-\sin x )(1+\sin x)=\cos^2x`

Therefore,
`(1-\sin x )(1+\sin x)=\cos^2x`

Answer 2

Finally...

(1-sin x )(1+sin x )

Now we have (1-sin(x)) (1+sin(x))

There is something call Expanded which is the way to write numbers by showing the value of each digit (google)

So let's us it to see what we find.

(1-sin(x)) (1+sin(x) that's equal 1-sin²(x)

We knew that 1-sin²(x) = cos²(x)

Answer : Cos²(x)

wow I did it guys :))

Hey I hope its help XD