Verify the identity
cos^2x-sin^2x=1-2sin^2x

From the basic definitions of sin and cos and the Pythagorean Theorem
cos2(x)+sin2(x)=1

or
cos2(x)=1−sin2(x)

So
cos2(x)−sin2(x)

=(1−sin2(x))−sin2(x)

=1−2sin2(x)
 
hope this helps. 

incomplete question. how do you expect anyone to you when you do not post the question in its entirety?

answer: what is the conflict?

step-by-step explanation:

*what has happened to new york city?

*what is in the time capsule?

* what did the kidz see that gave them hope?

*what will they do with what they find?

* how will they save the city?

* what challenges will they face along the way?

*what big choice will they make at the climax of the story?

* what lesson do they learn at the end of the story?