Question

Simplify (sinx + cosx) ^2/ sin2x

Answer 1

`\csc 2x+1`

Explanation:

• 
  `((\sin x+\cos x)^2)/(\sin2x)`

• We expand
  `(\sin x+\cos x)^2` using algebraic identity
  `(a+b)^2=a^2+b^2+2ab`

• 
  `=(\sin^2x+\cos^2x+2\sin x.\cos x)/(\sin2x)`

• 
  `= (1+\sin2x)/(\sin2x)`

• 
  `=(1)/(\sin2x)+(\sin2x)/(\sin2x)`

• 
  `=\csc 2x+1`