Circle all expressions that are equivalent to sin 4a 4 sin a

Circle all expressions that are equivalent to sin 4a. 4 sin a cos a 4 sin a cos a - 8 sin^3 a cos a sin a cos 3a - cos a sin 3a 2 sin 2a cos 2a 4 sin a cos a cos 2a 4 sin a cos^3 a-4 sin^3 a cos a Circle the expression that is equivalent to tan 3 pi/8. Squareroot 2 + 1 Squareroot 2 - l 1 - Squareroot 2 none of these Given that the exact value of sin pi/10 = -1 + Squreroot 5/4, for each question calculate the exact value of the given expression. You may leave nested radicals in your answer, hut rationalize any denominators.

Solution

16)sin4a

=2sin2a cos2a

sin4a

=2sin2a cos2a

=2(2sina cosa)(cos²a-sin²a)

=(4sina cosa)(cos²a-sin²a)

=4sinacos³a -4sin³acosa

sin4a

=2sin2a cos2a

=2(2sina cosa)(cos²a-sin²a)

=(4sina cosa)(cos²a-sin²a)

=(4sina cosa)(1-2sin²a)

=4sina cosa -8sin³a cosa