Prove that `(1)/(sin10^(0))-(sqrt(3))/(cos10^(0))=4`

(1)/(sin 10^(@)) - (sqrt3)/(cos 10 ^(@)) = 4.

Show that 1/(sin 10^@) - sqrt3/(cos 10^@) = 4

Prove that: sin18^0=(sqrt(5)-1)/4 .

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

Prove that (cos100sin10^0)/(cos10^0-s in 10^0)=tan55^0

Prove that : 4(sin^(-1)(1/sqrt(10)) + cos^(-1)( 2/sqrt(5)))=pi

Prove that: sin 65^0+cos 65^0=sqrt(2)cos 20^0

(i) If sin ^(-) x + sin ^(-1) y = pi//2 , then prove that : cos^(-1) x = sin^(-1) y (ii) Prove that : sin ((1)/(2) cos^(-1).(4)/(5))= (1)/sqrt(10) (iii) Prove that : tan ((1)/(2) cos^(-1).(sqrt(5))/(3)) = (3-sqrt(5))/(2)

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.

Prove that: sin36^0=(sqrt(10-2sqrt(5)))/4 .