Answer :

Zinethar
cotθ=1/tanθ=1/(sinθ/cosθ)=cosθ/sinθ <--- trig identity
secθ=1/cosθ <--- trig identity
cotθ*secθ=(cosθ/sinθ)*(1/cosθ)
cosθ/(sinθcosθ) <--- combine denominators
1/sinθ <--- cancel out the cosθ
csc=1/sinθ <--- trig identity
∴cotθ*secθ=cscθ

Answer:

Therefore, Verify.

Step-by-step explanation:

Given : cot θ ∙ sec θ = csc θ

To find : Verify the identity.

Solution : We have given

cot θ ∙ sec θ = csc θ

By the trigonometric identity : cot θ = [tex]\frac{cos(theta)}{sin(theta)}[/tex] .

sec θ = [tex]\frac{1}{cos(theta)}[/tex].

Then ,

Taking left hand side

cot θ ∙ sec θ

[tex]\frac{cos(theta)}{sin(theta)}[/tex] *  [tex]\frac{1}{cos(theta)}[/tex]

[tex]\frac{1}{sin(theta)}[/tex]

csc θ = right hand side.

Hence verify.

Therefore, Verify.

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