Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
θ=kπ,k∈Z
Alternative Form
θ=180∘k,k∈Z
Evaluate
csc(θ)cot(θ)=cos(θ)
Find the domain
More Steps
Evaluate
{θ=kπ,k∈Zcsc(θ)=0
Calculate
{θ=kπ,k∈Zθ∈R
Find the intersection
θ=kπ,k∈Z
csc(θ)cot(θ)=cos(θ),θ=kπ,k∈Z
Rewrite the expression
sin(θ)1sin(θ)cos(θ)=cos(θ)
Simplify the expression
sin(θ)cos(θ)sin(θ)=cos(θ)
Simplify the expression
cos(θ)=cos(θ)
The statement is true for any value of θ
θ∈R
Check if the solution is in the defined range
θ∈R,θ=kπ,k∈Z
Solution
θ=kπ,k∈Z
Alternative 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)1
Multiply 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)1
Cancel out the common factor sin(θ)
1
1cos(θ)
Divide the terms
cos(θ)
cos(θ)=cos(θ)
Solution
true
Show Solution
Graph
