Plzz fast i have exams tomorrow Q) sinx cosx=a Find sin4x+cos4x+sin6x+cos6x in terms of a - Maths - Some Applications of Trigonometry

Question

Plzz fast i have exams tomorrow
Q) sin x   cos x = a
Find sin 4 x + cos 4 x + sin 6 x + cos 6 x in terms of a

Abhishek Jha · Accepted Answer

Dear student,
Here is the solution of your asked query:
sinx cosx = a      {given}      
(i)Now we have;sin4x+cos4x=sin2x+cos2x2-2×sin2x×cos2x             {using the identity a2+b2=a+b2-2ab}=12-2sinx cosx2=1-2a2                    {using (i)}      
(ii)Also, sin6x+cos6x=sin2x3+cos2x3=sin2x+cos2xsin4x-sin2x×cos2x+cos4x    {using the identity a3+b3=a+ba2-ab+b2}=1sin4x+cos4x-sin2x×cos2x=1-2a2 -a2                           {using (i) and (ii)}       =1-3a2                                       
(iii)Adding (ii) and (iii) we get;  sin4x+cos4x+sin6x+cos6x=  1-2a2+1-3a2   =2-5a2       
Regards

Plzz fast i have exams tomorrow Q). sin x cos x = a Find sin 4 x + cos 4 x + sin 6 x + cos 6 x in terms of a.

Plzz fast i have exams tomorrow
Q). $\sin x \cos x = a$
Find $\sin^{4} x + \cos^{4} x + \sin^{6} x + \cos^{6} x$ in terms of a.