मान ज्ञात कीजिये :
(i) ` sin 75^(@)` (ii) ` tan 15^(@)`

Explanation

(i) ` sin 75^(@) = sin (45^(@) + 30^(@))`
` = sin 45^(2) cos 30^(@) + cos 45^(@) sin 30 ^(@)`
` = 1/(sqrt(2))* (sqrt(3))/2+ 1/(sqrt(2))*1/2 = (sqrt(3)+1)/(2sqrt(2))`
(ii) ` tan 15^(@) = tan (4^(2) - 30^(2))`
` = (tan 45^(@)- tan 30^(@))/(1+tan 45^(@) * tan 30^(@))= (1-1/(sqrt(3)))/(1+(1xx1/(sqrt(3))))`
` (1-1/(sqrt(3)))/(1+1/(sqrt(3)))= ((sqrt(3)-1)/(sqrt(3)))/((sqrt(3)+1)/(sqrt(3)))= (sqrt(3)-1)/(sqrt(3))xx(sqrt(3))/(sqrt(3)+1)`
` = (sqrt(3)-1)/(sqrt(3)+1) = (sqrt(3)-1)/(sqrt(3)+1)xx (sqrt(3)-1)/(sqrt3-1)`
` (sqrt(3)-1)^(2)/((sqrt(3))^(2)-(1)^(2))= (sqrt(3)^(2)+(1)^(2)-2*sqrt(3)*1)/(3-1)`
` = ( 4- 2 sqrt(3))/2 = 2- sqrt(3)`
अतः ` tan 15^(2) = 2 - sqrt(3)`