Question

what is sinX + cosX answer only one user

Answer 1

Answer:

Suppose that

sin

x

+

cos

x

=

R

sin

(

x

+

α

)

Then

sin

x

+

cos

x

=

R

sin

x

cos

α

+

R

cos

x

sin

α

=

(

R

cos

α

)

sin

x

+

(

R

sin

α

)

cos

x

The coefficients of

sin

x

and of

cos

x

must be equal so

R

cos

α

=

1

R

sin

α

=

1

Squaring and adding, we get

R

2

cos

2

α

+

R

2

sin

2

α

=

2

so

R

2

(

cos

2

α

+

sin

2

α

)

=

2

R

=

√

2

And now

cos

α

=

1

√

2

sin

α

=

1

√

2

so

α

=

cos

−

1

(

1

√

2

)

=

π

4

sin

x

+

cos

x

=

√

2

sin

(

x

+

π

4

)

Explanation:

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