Question

If √3theta =3sin theta then prove that sin2 theta -cos2 theta.

Answer 1

Apply the 2 trig identities:

sin (a + b) = sin a.cos b + sin b.cos a

cos (a + b) = cos a.cos b - sin a.sin b

sin

(

t

+

π

6

)

=

sin

t

.

cos

(

π

6

)

+

sin

(

π

6

)

.

cos

t

=

=

(

√

3

2

)

.

sin

t

+

cos

t

2

(1)

cos

(

t

+

π

3

)

=

cos

(

t

)

.

cos

(

π

3

)

−

sin

(

π

3

)

.

sin

t

=

=

cos

(

t

2

)

−

(

√

3

2

)

.

sin

t

.

(2)

Subtract (2) from (1), we get:

2

(

√

3

2

)

.

sin

t

=

√

3

.

sin

t