simplify sin^2θ/ 1-sin^2θ?

Question

prove that 1/tanθ + tanθ = 1/sinθcosθ

please could you include your working/notes so that i can under stand how you got yur answers because i really do not know how to do these. Thanks

Answer 1

sin^2θ/ 1-sin^2θ=sin^2θ/ cos^2θ=tan^2θ

1/tanθ + tanθ=(1+tan^2θ)/tanθ=(cos^2θ+sin^2θ)/sinθcosθ=1/sinθcosθ

Answer 2

sin^2θ/ 1-sin^2θ

(remember sin^2θ+cos^2θ=1)

=sin^2θ/ cos^2θ
=tan^2θ



1/tanθ + tanθ
=cos θ/sinθ + sinθ/cosθ
=(sin^2θ+cos^2θ)/(sin θ cosθ)
= 1/(sinθcosθ)


hint: tan θ=sinθ /cos θ

Answer 3

sin^2 t/*(1- sin^2 t) = sin^2 t/cos^2 t = tan ^2 t

using sin^2 t + cos^2 t= 1 and sin t/cost = tan t

2nd one)

1/tan t + tan t = cos t/sin t + sin t/cos t = (cos^2 t + sin ^2 t)/(sint cos t)
= 1/ (sin t cos t)