Find the value of the expression:- 3[sin^4 (3pi/2-x) + sin^4 (3pi+x)] -2 * [{sin^6 (pi/2+x) + sin^6 (5pi - x)] Share with your friends Share 25 Vijay Kumar Gupta answered this Consider the following expression. 3 sin43π2-x+sin43π+x-2 sin6π2+x+sin65π-xRewrite the above expression as, = 3 sin3π2-x4+sin3π+x4-2 sinπ2+x6+sin5π-x6 Note that, sin3π2-x=sinπ2+π-x =cosπ-x =-cosx sin3π+x=-sinx 3π+x lies in 3rd quadrant and sine is negative sinπ2+x=cosx sin5π-x=sinx 5π-x lies in 2nd quadrant and sine is positiveThis gives, = 3-cosx4+-sinx4-2 cosx6+sinx6 = 3cos4x+sin4x-2 cos6x+sin6x = 3cos4x+sin4x+2sin2x cos2x-2sin2x cos2x-2 cos2x3+sin2x3 Use the formulas, a2+b2+2ab=a+b2 a3+b3=a+b a2+b2-abThis implies that, = 3cos2x+sin2x2-2sin2x cos2x-2 cos2x+sin2x cos4x+sin4x-cos2x sin2x = 31-2sin2x cos2x-2 1 cos4x+sin4x-cos2x sin2x = 3-6sin2x cos2x-2cos4x+sin4x+2sin2x cos2x = 3-2cos4x+sin4x-4sin2x cos2x = 3-2cos4x+sin4x+2sin2x cos2x = 3-2cos2x+sin2x2 = 3-21 = 3-2 =1 81 View Full Answer
