Question

Please solve this for me.

Let f(x) = 3 sinx + 2. For any x1 belongs ro 0 to pi/2, there exists an x2 belongs to 0 to pi/2 such that
f(x1) + 2f (x2+theta) = 3

What could be the value of theta.?​

Answer 1

Step-by-step explanation:

cosx+sinx=

2

1

Divide both sides by cosx

1+tanx=

2cosx

1

Square both sides

(1+tanx)

2

=

4

sec

2

x

(1+tan

2

x+2tanx)4=sec

2

x=1+tan

2

x

After simplification

3tan

2

x+8tanx+3=0

D=d

2

=b

2

−4ac=64−36=28

d=±2

7

These are 2 real roots

tanx=

2a

−b

±

2a

d

=

6

−8

±

6

2

7

=

3

−4±

7

.