Question

If sin 0+ cos0= m then value of (sino - cos) is

Answer 1

Answer:

sinѲ - cosѲ = $\sqrt{m^{2}+2 }$

Step-by-step explanation:

sinѲ+cosѲ=m ----(1)

lets consider: sin0-cos0=n ------(2)

square the 1st equation:   $sin^{2}$Ѳ + $cos^{2}$Ѳ + 2sinѲcosѲ = $m^{2}$ -----(3)

square the 2nd equation:   $sin^{2}$Ѳ + $cos^{2}$Ѳ - 2sinѲcosѲ = $n^{2}$  ------(4)

Add 3rd and 4th equation:

                                       = $sin^{2}$Ѳ+$cos^{2}$Ѳ+$sin^{2}$Ѳ+$cos^{2}$Ѳ=$n^{2}$+$m^{2}$

                                    Since  $sin^{2}$Ѳ+$cos^{2}$Ѳ=1

                             ===>           1 + 1 =  $n^{2}$ +$m^{2}$

                             ===>          2 = $n^{2}$ +$m^{2}$

                             ===>           $n^{2}$ = $m^{2}$  +2

                             ===>            n = $\sqrt{m^{2}+2 }$

                             since          sinѲ - cosѲ = n

                             Therefore   sinѲ - cosѲ = $\sqrt{m^{2}+2 }$