Question

tan^3/1+tan^2+cot^3/1+cot^2 = 1-2 sin^2 cos^2x/sinx cosx​

Answer 1

Step-by-step explanation:

tan^3/1+tan^2+cot^3/1+cot^2

=tan^3/sec^2 + cot^3/cosec^2

=tan^3 cos^2 + cot^3 sin^2

=(sin^3/cos^3)cos^2 + (cos^3/sin^3)sin^2

=sin^3/cos + cos^3/sin

=(sin^4 + cos^4)/sin cos

=((sin^2)^2 +( cos^2)^2) /sin cos

=((sin^2)^2 +( cos^2)^2 +2sin^2 cos^2 - 2sin^2 cos^2) /sin cos

=((sin^2 +cos^2)^2 - 2sin^2 cos^2) / sin cos

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