Question : fraccot{theta}csc{theta} = costheta Solve the equation θ=kπ,k∈ZAlternative Form θ=180∘k,k∈Z Evaluate csc(θ)cot(θ)=cos(θ)Find the domain More Steps Evaluate {θ=kπ,k∈Zcsc(θ)=0Calculate {θ=kπ,k∈Zθ∈RFind the intersection θ=kπ,k∈Z csc(θ)cot(θ)=cos(θ),θ=kπ,k∈ZRewrite the expression sin(θ)1sin(θ)cos(θ)=cos(θ)Simplify the expression sin(θ)cos(θ)sin(θ)=cos(θ)Reduce the fraction cos(θ)=cos(θ)The statement is true for any value of θ θ∈RCheck if the solution is in the defined range θ∈R,θ=kπ,k∈ZSolution θ=kπ,k∈ZAlternative Form θ=180∘k,k∈Z Show Solution Verify the identity true Evaluate csc(θ)cot(θ)=cos(θ)Start working on the left-hand side More Steps Evaluate csc(θ)cot(θ)Use cott=sintcost to transform the expression csc(θ)sin(θ)cos(θ)Multiply by the reciprocal sin(θ)cos(θ)×csc(θ)1Multiply the terms sin(θ)csc(θ)cos(θ)Transform the expression More Steps Evaluate sin(θ)csc(θ)Use csct=sint1 to transform the expression sin(θ)×sin(θ)1Cancel out the common factor sin(θ) 1×1Multiply the terms 1 1cos(θ)Divide the terms cos(θ) cos(θ)=cos(θ)Solution true Show Solution Graph