Question

pove that.
tan3/1+tan2 + cot/1+cot2= sec.Cosec - 2 sin.Cas​

Answer 1

Step-by-step explanation:

LHS=tan3 θ/1 + tan2 θ + cot3 θ/1 + cot2 θ

= tan3 θ/sec2 θ + cot3 θ/cosec2 θ

= sin3 θ/cos3 θ × cos2 θ + cos3 θ/sin3 θ × sin2 θ

= sin3 θ/cos θ + cos3 θ/sin θ = sin4 θ + cos4 θ/sin θ.cos θ

= [sin2 θ + cos2 θ]2 – 2 sin2 θ. cos2 θ/sin θ.cos θ

= [(1)2 – 2 sin2 θ.cos2 θ]/sin θ.cos θ

= 1 – 2 sin2 θ.cos2 θ/sin θ.cos θ

= (1 – 2 sin2 θ.cos2 θ)/sin θ.cos θ

= 1/sin θ.cos θ = 2 sin2 θ.cos2 θ/sin θ.cos θ

= sec θ.cosec θ – 2 sin θ.cos θ

= R.H.S.

Hence proved.