Prove that 3(sin theta -cos theta)^4+6(sin theta+cos theta)^2 +4(sin^6theta+cos^6theta) is independent of theta - Maths - Introduction to Trigonometry

Question

Prove that 3(sin theta -cos theta)^4+6(sin theta+cos theta)^2
+4(sin^6theta+cos^6theta) is independent of theta

Brijendra Pal · Accepted Answer

Dear Student, 3sinx-cosx4+6sinx+cosx2+4sin2x3+cos2x3= 3sin2x+cos2x-2sinxcosx2+6sin2x+cos2x+2sinxcosx+4sin2x+cos2xsin4x+cos4x-sin2xcos2x=31-sin2x2+6+6sin2x+4sin2x+cos2x2-3sin2xcos2x= 3+3sin22x-6sin2x+6sin2x+6+4-12sin2xcos2x= 13+3sin22x-34sin2xcos2x= 13+3sin22x-3sin22x= 13So it is independent of angle xRegards

Prove that 3(sin theta -cos theta)^4+6(sin theta+cos theta)^2 +4(sin^6theta+cos^6theta) is independent of theta.