Question

a sin x + b cos x =??​

Answer 1

heyyy this is ur ans sinx /cos x = tan x hope it help. u

Answer 2

Explanation:

a

sin

x

+

b

cos

x

=

c

.

Dividing each term by

√

a

2

+

b

2

, we get the given equation

a

√

a

2

+

b

2

sin

x

+

b

√

a

2

+

b

2

cos

x

=

c

√

a

2

+

b

2

Now for solving such equation, assuming

cos

α

=

b

√

a

2

+

b

2

and

sin

α

=

a

√

a

2

+

b

2

.

Observe that it is compatible as

cos

2

α

+

sin

2

α

=

1

and

tan

α

=

a

b

or

α

=

tan

−

1

(

a

b

)

and then the given equation becomes

cos

x

cos

α

+

sin

x

sin

α

=

c

√

a

2

+

b

2

or

cos

(

x

−

α

)

=

c

√

a

2

+

b

2

and hence

x

−

α

=

2

n

π

±

cos

−

1

(

c

√

a

2

+

b

2

)

and

x

=

2

n

π

±

cos

−

1

(

c

√

a

2

+

b

2

)

+

α

or

x

=

2

n

π

±

cos

−

1

(

c

√

a

2

+

b

2

)

+

tan

−

1

(

a

b

)