Question

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

Answer 1

Answer:

$1 + 2 \times \sin(x ) \times \cos(x)$

Step-by-step explanation:

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

By expanding it , we get

${ \sin }^{2} x \: + { \cos }^{2} x \: + \: 2 \times \sin(x) \times \cos(x)$

we know that

${ \sin}^{2} x + { \cos }^{2} x = 1$

so,

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

Answer 2

Answer:

1 + sin2x

Step-by-step explanation:

Given

(sinx + cosx)² ← expand using FOIL

= sin²x + 2sinxcosx + cos²x

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

= 1 + sin2x