Question

(m+2)sin theta + (2m-1)cos theta=2m+1

Answer 1

Answer:

Let t=tan

2

2

θ

(m+2)sinθ+(2m−1)cosθ=2m+1

⇒(m+2)

1+t

2

2t

+(2m−1)

1+t

2

1−t

2

=2m+1

2mt+4t+2m−2mt

2

−1+t

2

=2m+2mt

2

+1+t

2

⇒(2t−1)(mt−1)=0

Gives t=

2

1

or t=

m

1

For t=tan

2

2

θ

=

2

1

⇒tanθ=

1−t

2

2t

=

1−

4

1

1

=

3

4

For t=tan

2

2

θ

=

m

1

⇒tanθ=

1−t

2

2t

=

1−

m

2

1

2

m

1

=2m(m

2

−1)