untitled

or,
2 3

2

2 n

2 s



 siA

coA

or,
3

1

n

s

siA

coA

or, cotA cot 60 $
? A 60 $
(c) Given that, A 45 $

we have to prove that,

ta A

ta A

co A 2

2

1 n

1 n

s 2





.H.S. =L cos 2 A

=cos(2u 45 $)=cos 90 $= 0

R.H.S. =
ta A

ta A

2

2

1 n

1 n





= $

$

1 n 45

1 n 45

2

2

ta

ta





= 2

2

1 1

1 1

()

()





=

2

0

= 0

∴L.H.S. = R.H.S. (proved)
(d) Given equation, 2 cos^2 θ 3 sinθ 3 0
or, 2 ( 1 sin^2 θ 3 ( 1 sinθ) 0
or, 2 ( 1 sinθ)( 1 sinθ) 3 ( 1 sinθ) 0
or,( 1 sinθ){2(1 sinθ) 3 } 0
or,( 1 sinθ){ 2 sinθ 1 } 0
or, 1 sinθ 0 or 2 sinθ 1 1
? sinθ 1 or, 2 sinθ 1

or,sinθ sin 90 $ or,

2

1

sinθ

? θ 90 $ or, sinθ sin 30 $
or, θ 30 $
θ is an acute angle, so θ 30 $.

Exercise 9⋅ 2

1. If
   2

1

cotθ , which one is the value of cotș?

(a)

3

1

(b) 1 (c) 3 (d) 2