10-3!

Double-Angle Formulas:

~sin2(alpha)=2sin(alpha)cos(alpha)

~cos2(alpha)=cos^2(alpha)-sin^2(alpha)

~cos2(alpha)=1-sin^2(alpha)

~cos2(alpha)=2cos^2(alpha)-1

~tan2(alpha)=2tan(alpha)/1-tan^2(alpha)

Half-Angle Formulas:

~sin(alpha)/2=+/-sqrt. of 1-cos(theta)/2

~cos(alpha)/2=+/-sqrt. of 1+cos(alpha)/2

~tan(alpha)/2=+/-sqrt. of 1-cos(alpha)/1+cos(alpha)

~tan(alpha)/2=sin(alpha)/ 1+cos(alpha)

~tan(alpha)/2=1-cos(alpha)/ sin(alpha)

You will use the formulas for all problems in section 10-3.

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Ex.1: Simplify:

~2sin(40)cos(40)

sin2(40)= sin80

Ex.2: Simplify:

~1-cos(10)/ sin(10)

tan(10)/2= tan5

Ex.3: SImplify:

~2cos^2(15)-1

cos2(15)= cos30

=sqrt. of 3/2