Prove: `(1-cos^2A)cos e c^2A=1`

Prove: (1-cos A)/(1+cos A)=(cot A-cos ecA)^(2)

Prove: (cos ecA)/(cos ecA-1)+(cos ecA)/(cos ecA+1)=2sec^(2)A

Prove that (1)cos2A=2cos^(2)A-1(2)cos2A=1-2sin^(2)A

prove that (1-cos2A)/(1+cos2A)=tan^(2)A

If A+B+C=0 , Prove : cos^2 A + cos^2 B +cos^2 C=1+2cosA cosB cosC .

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

If A+B+C= 360^(@) ,prove that: 1-cos^(2)A-cos^(2)B-cos^(2)C+2cosA cos B cos C=0

Prove: sqrt((1-cosA)/(1+cosA))+sqrt((1+cosA)/(1-cosA))=2 cos e c A

Prove that : cos^(2)A+cos^(2)(A+pi/3)+cos^(2)(A-pi/3) =1/2[2cos^(2)A+2cos^(2)(A+60^(@))+2cos^(2)(A-60^(@))] =1/2[1+cos2A+1+cos(2A+120^(@))+1+cos(2A-120^(@))] 1/2[3+cos2A+cos(2A+120^(@))+cos(2A-120^(@))] 1/2[3+cos2A+2cos(2A+120^(@)+2A-120^(@))/(2).cos(2A+120^(@)-2A+120^(@))/(2)] =1/2[3+cos2A+2cos2Acos120^(@)] =1/2[3cos2A+2cos2Acos(90^(@)+30^(@))] =1/2[3+cos2A-2.cos2A.(1/2)] =1/2(3+cos2A-cos2A) =3/2 = RHS Hence Proved.

If 2sec^2A-sec^4A-2cos e c^2A+cos e c^4A=(15)/4,t h e n tan A is equal 1//sqrt(2) (b) 1/2 (c) 1/2sqrt(2) (d) -1/(sqrt(2))