` sin 37(1^(@))/2 * sin 7 (1^(@))/2` का मान ज्ञात कीजिए ।

Options

A. ` (sqrt(3)-sqrt(2))/4`
B. ` (sqrt(3)-sqrt(2))/5`
C. ` (sqrt(7)-sqrt(2))/4`
D. ` (sqrt(3)-sqrt(5))/4`

Answer

A

Explanation

` sin 37 (1^(@))/2 * sin 7 (1^(@))/2`
` = 1/2 * 2 sin 37 (1^(@))/2 * sin7 (1^(@))/2`
` = 1/2 * [ cos ( 37 (1^(@))/2 - 7 (1^(@))/2)- cos (37 (1^(@))/2 + 7 (1^(@))/2)]`
` = 1/2 (cos 30^(2)- cos 45^(@))`
` = 1/2 (sqrt(3)/2 - 1/(sqrt(2)))= (sqrt(3)-sqrt(2))/4`