Show that : `sin^8 A-cos^8 A = (sin^2 A - cos^2 A) (1-2 sin^2 A*cos^2 A)`

Show that (i) sin^(8)A-cos^(8)A=(sin^(2)A-cos^(2)A)(1-2sin^(2)A.cos^(2)A) (ii) (1)/(sec A-tan A)-(1)/(cos A)=(1)/(cos A)-(1)/(sec A + tan A)

(1- sin A - cos A)^2 = 2 (1-sin A) (1-cos A)

Prove the following identities: sin^4A-cos^4A=sin^2A-cos^2A=2sin^2A-1=1-2cos^2A

Prove the following identities : (sin A + cos A)/ (sin A - cos A) + (sin A - cos A)/ (sin A + cos A) = (2)/ (2 sin^(2) A - 1)

int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=

int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=

(1+sin2A-cos2A)/(1+sin2A+cos2A)=tanA

Prove that : (1)/ (sin A - cos A) - (1)/ (sin A + cos A) = (2 cos A)/(2 sin^(2) A - 1)

Solve (1+sin^2x-cos^2x)/(1+sin^2x+cos^2x)

If A = 30^(@) , show that : (i) (1 + sin 2A + cos 2A)/(sin A + cos A) = 2 cos A (ii) (cos^(3)A - cos 3A)/(cos A) + (sin^(3)A + sin 3A)/(sin A) = 3