`(sin 15^(@) cos 75^(@) + cos 15^(@) sin 75^(@))/(tan 5^(@) tan 30^(@) tan 35^(@) tan55^(@)tan 85^(@))`का मान निकालें ।

Explanation

`(sin 15^(@) cos 75^(@) + cos 15^(@) sin 75^(@))/(tan 5^(@) tan 30^(@) tan 35^(@) tan55^(@)tan 85^(@))`
` = (sin 15^(@) cos (90^(@) - 15^(@))+cos 15^(@) sin (90^(@) - 15^(@)))/(tan 5^(@) . 1/sqrt3* tan 35^(@) tan (90^(@) - 35^(@))* tan(90^(@) - 5^(@)))`
` [cos (90^(@) - theta) = sin theta, sin (90^(@) - theta ) = cos theta , tan (90^(@) - theta ) = cot theta , tan theta = 1/(cot theta) ]`
` = (sin 15^(@) * sin 15^(@) + cos 15^(@) * cos 15^(@))/(1/(cot 5^(@))*1/sqrt3 *1/(cot 35^(@))*cot 35^(@) * cot 5^(@))`
` = (sin^(2) 15^(@) + cos ^(2) 15^(@))/(1/sqrt3) = 1 xx sqrt3/1 = sqrt3 " "[:' sin^(2 theta) + cos^(2 theta) = 1]`