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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