Prove: 1/cot^2θ - 1/csc^2θ = sin^4θ/cos^2θ ??

1 Answer
Feb 25, 2018

#LHS=1/cot^2θ - 1/csc^2θ#

#=sin^2 theta/(cos^2θ) - sin^2θ#

#=sin^2 theta(1/(cos^2θ) - 1)#

#=(sin^2 theta(1-cos^2θ))/ cos^2theta#

#=(sin^2 theta*(cos^2theta+sin^2theta-cos^2θ))/ cos^2theta#

#=(sin^2 theta*sin^2θ)/ cos^2theta#

# = sin^4θ/cos^2θ =RHS#

Formula used

  • #cottheta=costheta/sintheta#

  • #csctheta=1/sintheta#

  • #cos^2theta+sin^2theta=1#