Question

Cos 5A +Cos3A =0 find the value of A .

Answer 1

cos5A+cos3A=0
or, 2cos(5A+3A)/2cos(5A-3A)/2=0
or, 2cos4AcosA=0
or, cos4AcosA=0
Either, cosA=0
or, cosA=cosπ/2
or, A=π/2
Or, cos4A=0
or, 2cos^2(2A)-1=0
or, 2cos^2(2A)=1
or, cos^2(2A)=1/2
or, cos2A=+-1/√2
Thus either, cos2A=1/√2
or, cos2A=cosπ/4
or, 2A=π/4
or, A=π/8
Or, cos2A=-1/√2
or, cos2A=-π/4
or, cos2A=cos(π-π/4)
or, 2A=π-π/4
or, 2A=3π/4
or, A=3π/8
Then, A= π/2, π/8, 3π/8 Ans.