Question

cos(2x)+2sin^2(x)+1

Answer 1

You know at least two formulas for cos(2x).
Choose the one which turns it into something with sin²x. Why? Because you have more of these in your problem!

Answer 2

i got 1-2sin^2x+2sin^2x+1

Answer 3

Right! Now see if you still can count...

Answer 4

2sin^x?

Answer 5

Look at the middle two terms... what will happen?
Hint: it's easy as 1+1!

Answer 6

i have no idea :/

Answer 7

You have something of the form:

1 - A + A + 1.

What is the answer of that?

Answer 8

1+A+1

Answer 9

How can that be?
I'll make it more clear: suppose A= 4.

Then you have :

1 - 4 + 4 + 1.

What is the answer?

Answer 10

0

Answer 11

2

Answer 12

- 4 + 4 = 0, but there is also 1 in the beginning and 1 in the end. They add up to 2.

So:

1 - 4 + 4 + 1 = 1 + 0 + 1 = 2

Also:

1 - A + A + 1 = 1 + 0 + 1 = 2

Now you calculate:

1 - 2sin²x + 2sin²x + 1

Answer 13

2?

Answer 14

Right! See? The middle two terms are opposite, so when you add them up, they give 0.
So the answer is 1+1=2.