o it is necessary to "submit" after filling in each blank. The quickest way to do this is hit enter after typing instead of pushing the submit button.

Please see formatting instructions below the problem.

Use the double angle identities
cos ( 2 x )

cos 2 ( x ) − sin 2 ( x ) and
sin ( 2 x )

2 sin ( x ) cos ( x ) to verify the double angle identity
tan ( 2 x )

2 tan ( x ) 1 − tan 2 ( x )

The left side makes it easier to use the two identities given to us, so start there:	  

tan ( 2 x )

=

1. Rewrite
   tan ( 2 x ) using a quotient identity: Correct =

   Now you have sin ( 2 x ) cos ( 2 x )

=

2. Rewrite the left side using the two double angle identities given at the beginning: Correct =

   Now you have 2 sin ( x ) cos ( x ) cos 2 ( x ) − sin 2 ( x )

=

3. The denominator on the left side of the identity will become exactly the denominator on the right side if it is divided by what? Correct

4. Multiply the left side by
   1 cos 2 ( x ) 1 cos 2 ( x ) which is a sneaky way of multiplying by 1. 2 sin ( x ) cos ( x ) cos 2 ( x ) − sin 2 ( x )

Incorrect

Now you have	  

2 sin ( x ) cos ( x ) cos 2 ( x ) − sin 2 ( x ) ⋅ 1 cos 2 ( x )

=

5. Multiply the two fractions, but do not simplify yet. (Note: you will get a fraction in the numerator and a fraction in the denominator) : Incorrect =

   Now you have 2 sin ( x ) cos ( x ) cos 2 ( x ) ( 1 − tan 2 ( x ) )

=

6. Fully simplify the numerator and denominator. Then you have proven the identity! Correct

FORMATTING INSTRUCTIONS BELOW Type in lowercase and use parentheses. For example type sin(x) not sinx.

For fractions use the divide symbol "/". For example sin(x)/cos(x) for
sin ( x ) cos ( x )

For multiplication of fractions use parentheses. For example (cos(a)/sin(b))(tan(c)/sin(d)) for
( cos ( a ) sin ( b ) ) ( tan ( c ) sin ( d ) ) .

For multiplication without fractions no symbol is necessary. For example cos(a)sin(b)

For exponents use "^". Parentheses will be necessary depending on how you choose to type your answer For example sin^2(x) for
sin 2 ( x ) . Or (sin(x))^2 for
( sin ( x ) ) 2 . For fractions with multiple terms in the numerator or denominator parentheses are necessary. For example (1+sin(x))/cos(x) for
1 + sin ( x ) cos ( x ) . Or (1+sin(x))/(1-sin(x)) for
1 + sin ( x ) 1 − sin ( x )