Question

If cot4A-cot2A=1 then cos4+cos2A=?​

Answer 1

Answer:

cot^4 A - cot^2 A = 1

cos^4 A/sin^4 A - cos^2 A/sin^2 A = 1

(cos^4 A - cos^2 A sin^2 A)/sin^4 A = 1

cos^4 A - cos^2 A sin^2 A = sin^4 A

cos^4 A - cos^2 A sin^2 A - sin^4 A = 0

cos^4 A - (cos^2 A + sin^2A)sin^2 A = 0

cos^4 A - sin^2 A = 0

cos^4 A - (1 - cos^2 A) = 0

cos^4 A -1 + cos^2 A = 0

cos^4 A + cos^2 A = 1.

Step-by-step explanation:

cot^4A-cot^2A=1

cos^4A/sin^4A - cos^2A/sin^2 A=1

cos^4A-cos^2A . sin^2A = sin^4A

cos^4A = sin^4A + cos^2A . sin^2A

cos^4A + cos ^2A = sin^4A + cos^2A . sin^2A + cos ^2A

=sin^4A + cos^2A (1+sin^2A)

=sin^4A + (1 - sin^2A) (1+sin^2A)

=sin^4A + 1 - sin^4A = 1