Solution : Given that, tanA 1.
So, opposite side of the A = 1, adjacent side = 1

hypotenuse = 12  12 2

Therefore, sinA=
2

1

, cosA=

2

1

.

Now left hand side = 2 sinAcosA= 2
2

1

˜

2

1

˜ = 2

2

1

˜ = 1

= right hand side.
= 2 sinAcosA 1 is a true statement.

Activity :

1. If ‘C is a right angle of a right angled triangle ABC, AB=29 cm, BC= 21
   cm and ‘ABC θ, find the value of cos^2 θsin^2 θ.

Example 4. Prove that, tanθcotθ secθ,cosecθ.
Proof :
Left hand side = tanθcotθ

=
θ

θ

θ

θ

sin

cos

cos

sin



=
θ θ

θ θ

sin cos

sin^2 cos^2

˜



=
sinθ cosθ

1

˜

[sin^2 θcos^2 θ 1 ]

=
θ cosθ

1

sin

1

˜

=cosecθ˜secθ
=secθ˜cosecθ=
= R.H.S. (proved)

Example 5. Prove that, 1
1 cosec

1

1 sin

1

^2 θ ^2 θ^

Proof : L.H.S. =

(^2) θ 1 cosec (^2) θ
1
1 sin
1




θ
θ
2
2
sin
1
1
1
1 sin
1




θ
θ
θ^2
2
(^21) sin
sin
1 sin
1