`|["sin"23^(@), -"sin"7^(@)], ["cos"23^(@), "cos"7^(@)]|=?`

The value of ("sin"23^(@)"cos"67^(@)"tan"45^(@)+"cos"23^(@)"sin"67^(@)"cot"45^(@))/(2"sin"45^(@)"cos"45^(@)) is:

Prove the following identities : 4 sin 23^(@) sin37^(@) sin 83^(@) = cos21^(@)

The value of the determinant Delta=|{:(sin^(2)23^(@)" "sin^(2)67^(@)" "cos180^(@)),(-sin^(2)67^(@)" "-sin^(2)23^(@)" "-cos180^(@)),(cos180^(@)" "sin^(2)23^(@)" "sin^(2)67^(@)):}| is

cos7^(@)cos23^(@)cos45^(@)cosec83^(@)cosec67^(@)=?

The value of (sin 20^(@)cos70^(@)+ cos20^(@)sin70^(@))/(sin23^(@)"cosec"23^(@)+cos23^(@)sec23^(@)) is _________.

The value of (sin 1^(@) + sin 3^(@) + sin 5^(@) + sin 7^(@))/( cos 1^(@) .cos2^(@).sin4^(@)) is"________"

(1)/(4)[sqrt(3)cos23^(@)-sin23^(@)]=

The value of (sin 1^(@) +sin 3^(@) + sin 5^(@) +sin 7^(@))/(cos 1^(@)*cos 2^(@)sin 4^(@)) is __________

The value of (sin 1^(@) +sin 3^(@) + sin 5^(@) +sin 7^(@))/(cos 1^(@)*cos 2^(@)sin 4^(@)) is __________