Prove that
`(i) " 2 cos " 45^(@) " cos " 15^(@)=((sqrt(3)+1))/(2) " "(ii) 2 " sin " 75^(@) " sin " 15^(@)=(1)/(2)`
`(iii) " cos " 15^(@) - " sin " 15 =(1)/(sqrt(2))`

Prove that (i) " sin " 80^(@) "cos " 20^(@) - " cos " 80^(@) " sin " 20^(@) =(sqrt(3))/(2) (ii) " cos " 45^(@) " cos " 15^(@) - " sin " 45^(@) " sin " 15^(@) = (1)/(2) (iii) " cos " 75^(@) " cos " 15^(@) + " sin " 75^(@) " sin " 15^(2)= (1)/(2) (iv) " sin " 40^(@) " cos " 20^(@) " + cos " 40^(@) " sin " 20^(@) =(sqrt(3))/(2) (v) " cos " 130^(@) " cos " 40^(@) l + " sin " 130^(@) " sin " 40^(@) =0

Prove that cos 15 ^(@) - sin 15^(@) = (1)/(sqrt2)

cos^(2) 45^(@) - sin^(2) 15^(@)=

( sin 75^(@) - sin 15^(@))/( cos 15^(@) - cos 75^(@))=

Prove : cos15^(@) - sin15^(@) = 1//sqrt2 .

Prove that : (i) "sin"105^(@)+cos105^(@)=(1)/(sqrt(2)) (ii) cos105^(@)+cos15^(@)="sin"75^(@)-"sin"15^(@)

Prove that (i) "cos " 15^(@) - " sin " 15^(@) = (1)/(sqrt(2)) (ii) " cot " 105^(@) - " tan " 105^(@) =2sqrt(3) (iii) (tan 69^(@) + tan 66^(@))/(1-tan 69^(@) tan 66^(@)) =-1

Prove that sin 75^(@) - sin 15^(@) = cos 105^(@) + cos 15^(@)

(sin75^(@) - sin 15^(@))/(cos 75^(@) + cos 15^(@)) A) -sqrt3 B) sqrt3 C) (1)/(sqrt3) D) (1)/(sqrt3)

cos ^ (2) 45 ^ (@) - sin ^ (2) 15 ^ (@) =