(i) sin (75°) = sin (30° + 45°) = sin 30° cos 45° + cos 30° sin 45°
[Since sin (A + B) = sin A cos B + cos A sin B]
=

1

2

×

1

√2

+

√3

2

×

1

√2

=

1

2√2

+

√3

2√2

=

1+√3

2√2

(ii) tan 15° = tan (45° – 30°)
=

tan45°−tan30°

1+tan45°tan30°

=

1− 1 √3

1+1× 1 √3

=

√3−1

√3+1

= 2 - √3