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f(x) = sin x + cos x, then find the most general solution of
f(x) = [f(pi/10)]. [.] is greatest integer function
Dear
f(pi/10) =sin18 + cos18
=√2 sin(45+18) =√2sin63
we know sin63>sin45=1/√2
and sin63 <1
so 1<√2sin63<2
so [√2sin63] =1
now equation become
sinx +cosx =1
cos(x-∏/4) =1/√2
cos(x-∏/4) =cos∏/4
x-∏/4 =2n∏ ± ∏/4
x =∏/4 +2n∏ ± ∏/4
x = 2n∏ and 2n∏ +∏/2
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