Question

Which of the following number (s) is/are rational? A) sin 15° B) cos 15° C) sin15° cos15° D) sin 15° cos 75°

Answer 1

Option (C).

Sin 15 cos 15 can be written as

= 1/2 2 sin 15 cos 15  (2 sin a cos a = sin 2a)

= 1/2 sin (2 * 15)

= 1/2 sin 30

= 1/2 * 1/2

= 1/4.

Answer 2

Answer:

$\sin 15 ^ { \circ } \cos 15 ^ { \circ }$ is the correct option

To find:

Which out of the given option is/are rational number/s = ?  

Solution:  

Given :  

Sin 15 , cos 15, sin 15 cos 75 all involves √3. Hence, the said nos. are irrational.

Option C :  

$\sin 15 ^ { \circ } \cos 15 ^ { \circ } = \frac { 1 } { 2 } 2 \sin 15 ^ { \circ } \cos 15 ^ { \circ }$

We know that

$2 \sin 15 ^ { \circ } \cos 15 ^ { \circ } = \sin 30 ^ { \circ }$

Thus,

$\frac { \sin 30 ^ { \circ } } { 2 } = \frac { 1 } { 4 } = 0.25$

which is rational number.

$\sin 15 ^ { \circ } \cos 15 ^ { \circ }$ is the rational number . Hence , option C is the correct one .