Question

Find value of sin 75° cos 15° - cos 75° sin 15°
1. \(\frac {\sqrt 3 + 1}{2}\)
2. \(\frac {\sqrt 3}{2}\)
3. 1
4. 0

Answer 1

Correct Answer - Option 2 : \(\frac {\sqrt 3}{2}\)

Concept:

sin x cos y + cos x sin y = sin (x + y)

sin x cos y - cos x sin y = sin (x - y)

Calculation:

Here, we have to find the value of sin 75° cos 15° - cos 75° sin 15°

As we know that, sin x cos y - cos x sin y = sin (x - y)

∴ sin 75° cos 15° - cos 75° sin 15° = sin (75° - 15°)

= sin 60° 

= \(\frac {\sqrt 3}{2}\)