4.Prove that: `(1)/(sin10^(@))-(sqrt(3))/(cos10^(@))=4`

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

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

Prove that (sin20^(@) + sin40^(@)) + (cos20^(@) + cos40^(@))=(sqrt(3)+1)cos10^(@)

(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)

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

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

Prove that: (cos80^@)/(sin10^@)+cos59^@\ cosec\ 31^@=2

Prove that sqrt(10)[(sqrt(10)+1)^(100)-(sqrt(10)-1)^(100)] is an even integer .

Prove that sqrt(10)[(sqrt(10)+1)^(100)-(sqrt(10)-1)^(100)] .

Prove that: i) sin50^(@)-sin70^(@)+sin10^(@)=0 ii) sin(60^(@)+A)+sin(60^(@)-A) = sqrt(3)cosA