Question

Simplify the following expression: (sin x + cos x)^2

Answer 1

`1 + 2 * \sin(x ) * \cos(x)`

Explanation:

`( \sin(x) + \cos(x) \: )^(2)`

By expanding it , we get

`{ \sin }^(2) x \: + { \cos }^(2) x \: + \: 2 * \sin(x) * \cos(x)`

we know that

`{ \sin}^(2) x + { \cos }^(2) x = 1`

so,

`{ \sin }^(2) x + { \cos}^(2) x + 2 * \sin(x) * \cos(x) = 1 + 2 * \sin(x) * \cos(x)`

Answer 2

1 + sin2x

Explanation:

Given

(sinx + cosx)² ← expand using FOIL

= sin²x + 2sinxcosx + cos²x

[ sin²x + cos²x = 1 and sin2x = 2sinxcosx ]

= 1 + sin2x