Prove that: `cos18^0-sin 18^0=sqrt(2)sin27^0`

If cos theta+sin theta=sqrt(2)cos theta then prove that cos theta-sin theta=sqrt(2)sin theta

Prove that (cos10^0+sin10^0)/(cos10^0-sin 10^0)=tan55^0

Prove that: sin10^0sin30^0sin50^0sin70^0=1/(16)dot

Prove that sin 12^(@) sin18^(@)sin42^(@) sin48^(@) sin 72^(@) sin78^(@)=(cos18^(@))/(32) .

(a) Prove that sin65^(@)+cos65^(@)=sqrt(2)cos 20^(@) (b) Prove that sin47^(@)+cos77^(@)=cos17^(@)

Prove that (i) sin A+sin (120^(@)+A)+sin(240^(@)+A)=0 (ii) cos A+cos (120^(@)+A)+cos (120^(@)-A)=0

Prove that : sin A + sin(120^@ + A) + sin(240^@ + A) = 0

If cosx=tany ,coty=tanz ,cotz=tanx , then the value of sinx is (a) 2cos18^0 (b) cos18^0 (c) sin18^0 (d) 2sin18^0

Prove that sin 50^(@)-sin 70^(@)+cos 80^(@)=0 .

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))