Formulae `sin2A`, `cos(2A)` & `tan(2A)`

Geometrical proOF OF double angle(sin2A,cos2A,tan2A) and question based on this

(1 + sin2A-cos2A) / (1 + sin2A + cos2A) = tan A

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

Prove :sin^(2)A cot^(2)A+cos^(2)A tan^(2)A=1

Prove that (sin2A)/(1+cos2A)=tan A

(sin A + sin2A) / (1 + cos A + cos2A) = tan A

If cosA=24/25 , evaluate the following, given that 0 lt A lt pi/2 . i) sin2A ii) cos 2A iii) tan 2A

If A=30^(@), prove that sin2A=2sin A cos A=(2tan A)/(1+tan^(2)A)

By using above basic addition/ subtraction formulae, prove that (i) tan (A+B)=(tan A+tan B)/(1-tan A tan B) , (ii) tan (A-B)=(tan A-tanB)/(1+tan A tan B) (iii) sin2theta=2sintheta costheta , (iv) cos2theta=cos^(2)theta=1-2sin^(2)theta=2cos^(2)theta-1 (v) tan 2theta=(2 tan theta)/(1-tan^(2) theta)

(cos A + sin A) / (cos A-sin A) - (cos A-sin A) / (cos A + sin A) = 2tan2A