C httpswwwwebassignnetwebStudentAssignmentResponsessu Simpl

(--) C https://www.webassign.net/web/Student/Assignment-Responses/su Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula. (a) 2 sin 180 cos 18 (b) 2sin 39 cos 30 10. ·0/10 points ! Previous Answers SAgTrig3 83 031 Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula. (a) cos2 31°-sin2 31 Remember to use a degree symbol. (b) cos2 68-sin2 6e Need Help?Read ItWatch It Talk to a Tutor Search the web and Windows

Solution

1) 2 sin 18 cos 18

applying double angle formula

sin 2 a = 2 sin a cos a

therefore , 2 sin 18 cos 18 = sin 2(18) = sin 36

b) 2 sin 3 theta cos 3 theta

sin 2 a = 2 sin a cos a

2 sin 3 theta cos 3 theta = sin 2(3 theta ) = sin 6 theta

10. a ) cos^2 31 - sin^2 31

cos^2 a - sin^2 a = cos 2a

therefore , cos^2 31 - sin^2 31 = cos 2(31) = cos 62

b) cos^2 ( 6 theta ) - sin^2 (6 theta )

cos^2 a - sin^2 a = cos 2a

therefore, cos^2 ( 6 theta ) - sin^2 (6 theta ) = cos 2 ( 6 theta ) = cos 12 theta