wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The numerical value of 3(sinxcosx)4+6(sinx+cosx)2+4(sin6x+cos6x) is​​​​​​​

Open in App
Solution

3(sinxcosx)4+6(sinx+cosx)2+4(sin6x+cos6x)
Let
A=3(sinxcosx)4A=3[(sinxcosx)2]2A=3(12sinxcosx)2A=3(14sinxcosx+4sin2xcos2x)A=312sinxcosx+12sin2xcos2x(1)

B=6(sinx+cosx)2B=6(1+2sinxcosx)B=6+12sinxcosx(2)

C=4(sin6x+cos6x)C=4((sin2x)3+(cos2x)3)C=4{(sin2x+cos2x)33sin2xcos2x(sin2x+cos2x)}[x3+y3=(x+y)33xy(x+y)]C=4(13sin2xcos2x)C=412sin2xcos2x(3)
So,
3(sinxcosx)4+6(sinx+cosx)2+4(sin6x+cos6x)=A+B+CFrom equation (1), (2) and (3)A+B+C=13


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon