UPSC NDA Math Model Paper 9

sin 15° sin 75°
= sin 75° sin 15°
= sin (90° - 15°). sin 15°
= cos 15°. sin 15°
Multiply and divide by 2, we get
=

1

2

2. cos 15°. sin 15°
=

1

2

2. sin 15°. cos 15°
We know that
sin 2θ = 2 sin θ cos θ
=

1

2

× sin 2(15°)
=

1

2

× sin (30°)
=

1

2

×

1

2

=

1

4

Hence, the value of sin 15° sin 75° is =

1

4