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padilas [110]
3 years ago
13

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

Mathematics
2 answers:
valina [46]3 years ago
6 0

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)

guajiro [1.7K]3 years ago
4 0

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

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