Prove that : `cos 9^0 + sin 9^0 = sqrt(2) sin 54^0`

Prove that: cos18^(@)-sin18^(0)=sqrt(2)sin27^(0)

Prove that: cos18^(@)-sin18^(0)=sqrt(2)sin27^(0)

Prove that : sin 75^0 = (sqrt(6) + sqrt(2))/4

Prove that (cos 9^(@)+ sin 9^(@))/(cos 9^(@) -sin 9^(@)) = tan 54^(@)

" Prove that "(cos9^(0)+sin9^(0))/(cos9^(0)-sin9^(0))=cot36^(@)

Without using trigonometric tables, prove that : (i) cos -81^@-sin 9^@=0 (ii) tan 71^@-cot 19^@=0 (iii) cosec 80^@-sec 10^@=0 (iv) cosec ^2 72^@-tan^2 18^@=1 (v) cos^2 75^@ +cos ^2 15^@=0 (vi) tan^2 66^@-cot^2 24^@=0 (vii) sin^2 48^@+sin^2 42^@=1 (viii) cos^2 57^@-sin^2 33^@=0 (ix) (sin 65^@+cos 25^@)(sin 65^@-cos 25^@)=0

sin9^(@)+cos9^(@)=sqrt(2)sin54^(@)

Prove that: (cos8^(0)+sin8^(0))/(cos8^(0)-sin8^(@))=tan37^(0)

Prove that: (cos11^(0)+sin11^(0))/(cos11^(0)-sin11^(0))=tan56^(@)

Prove that: cos^(2)48^(0)-sin^(2)12^(0)=(sqrt(5)+1)/(8)