untitled

(b) If
1 3

1 3

cosA sinA

cosA sinA









, find the value of A.

(c) Prove that,
1 tanA

1 tanA

cos 2 A 2

2





, if A 45 $.

(d) Solve : 2 cos^2 θ 3 sinθ 3 0 , where θ is an acute angle.

Solution : (a) 2 cos(AB) 1

or,

2

1

cos(AB)

or,cos(AB) cos45$ [

2

1

cos45$ ]

? AB 45 $..................(i)

and 2 sin(AB) 3

or,

2

3

sin(AB)

or,sin(AB) sin 60 $ [

2

3

sin 60 $ ]

? AB 60 $....................(ii)

Adding (i) and (ii), we get,

2 A 105 $

?

2

105 $

A

$

2

1

52

Again, subtracting (i) from (ii), we get
2 B 15 $

or,
2

15 $

B

?

$

2

1

B 7

Required

$

2

1

A 52 and

$

2

1

B 7

(b)
1 3

1 3

s n

s n









coA siA

coA siA

or,
1 3 1 3

1 3 1 3

s n s n

s n s n

  

  

  

  

coA si A coA siA

coA siA coA siA