Question

Find the value of a, 0°<= a =<90°.
question: sin4a = cos2a​

Answer 1

`\textsf{sin4a = cos2a}\\\textsf{or, 2 sin2a cos2a = cos2a}\\\textsf{or, 2 sin2a cos2a - cos2a = 0}\\\textsf{or, cos2a(2sin2a - 1) = 0}\\\textsf{i.e. cos2a = 0 or 2sin2a - 1 = 0}\\`

`\textsf{When cos2a = 0, cos2a = cos90}^o\textsf{ or, 2a =90}^o \textsf{ or, a = 45}^o`

`\sf{When\ 2sin2a - 1 = 0,} \\\\\sf{\ \ \ \ \ }sin2a = (1)/(2)\ \\\\or,\ sin2a=sin30^o,\ sin150^o\ \\or,\ 2a=30^o,150^o\\\ or,\ a=15^o,75^o`

`\sf{\therefore\ a=15^o,45^o, 75^o}`