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let sinx=s and cosx=c
we know that c^12
and s^2, s^4, s^6>=0
adding these inequalities, we get
(1 – c^12)+s^2+s^4+s^6>=0
or (1+s^2)(1+s^4)>=c^12
multiplying booth sides by c^2>=0,
c^2*(1+s^2)(1+s^4)>=c^12*c^2
or (1 – s^2)(1+s^2)(1+s^4)>=c^14
(1 – s^4)(1+s^4)>=c^14
1 – s^8>=c^14
or c^14+s^8
or A
and as s^8, c^14>=0, adding we get
s^8+c^12>=0
so,
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