Show that `sin A = sqrt(1-cos^2 A)`.

Show that : sin 30^(@)=sqrt((1-cos60^(@))/(2))

If tan A=sqrt(2)-1 show that sin A cos A=(sqrt(2))/(4)

For A=460^(@), show that 2sin((A)/(2))=-sqrt(1+sin A)-sqrt(1-sin A)

Show that (i) sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x ,-1/(sqrt(2))lt=xlt=1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^2))=2cos^(-1)x ,1/(sqrt(2))lt=xlt=1

If a cos x-b sin x=c show that a sin x+b cos x=sqrt(a^(2)+b^(2)+c^(2))

Show that (1+sin A)/(cos A)+(cos B)/(1-sin B)=(2sin A-2sin B)/(sin(A-B)+cos A-cos B)

Show that : Cos^4A - Sin^4A = Cos^2A - Sin^2A = 2 Cos^2A - 1

If A=340^(@), prove that 2sin((A)/(2))=-sqrt(1+sin A)+sqrt(1-sin A) and 2cos((A)/(2))=-sqrt(1+sin A)-sqrt(1-sin A)

Prove that (1)cos36^(@)cos72^(@)cos108^(@)cos144^(@)=(1)/(16)(2) Show that 4sin27^(@)=sqrt(5+sqrt(5))-sqrt(3-sqrt(5))

Show that sin 150^(@) + cos 105^(@) =(1)/(sqrt(5))