Question

If 4 sin x. cos y + 2 sinx + 2 cos y + 1 = 0 where x,y € [0,21] find the largest possible value
of the sum (x + y).
s​

Answer 1

Step-by-step explanation:

:

Factor

4

sin

x

cos

x

+

2

sin

x

−

2

cos

x

−

1

=

0

as

(

2

sin

(

x

)

−

1

)

(

2

cos

(

x

)

+

1

)

=

0

then solve the two terms using standard trig values.

2

sin

(

x

)

−

1

=

0

→

sin

(

x

)

=

1

2

→

x

=

30

o

or

x

=

150

o

or

2

cos

(

x

)

+

1

=

0

→

cos

(

x

)

=

−

1

2

→

x

=

120

o

or

x

=

240

o

Answer 2

Step-by-step explanation:

If

sin x/sin y = 1/2 , cos x/cos y = 3/2

where

x,y ∈ (0'π/2),

then the value of

tan(x+y),

is equal to