The simplest form of the given expression is Cot θ. Using trigonometric functions the complex expressions can be simplified into a simpler form.
What are the trigonometric functions?
The trigonometric functions are as follows:
Sin θ = 1/Csc θ
Cos θ = 1/Sec θ
Tan θ = Sin θ/Cos θ
Cot θ = 1/Tan θ = Cos θ/Sin θ
Sec θ = 1/Cos θ
Cosec θ = 1/Sin θ
Calculation:
The given expression is
[{(Cot θ)(Cos θ)}/Sin θ × tan θ] ÷ [(Sin θ)/(Cos θ)(tan θ)]
Simplifying the first term:
[{(Cot θ)(Cos θ)}/Sin θ × tan θ]
⇒ (Cot θ) × (Cos θ/Sin θ) × tan θ
Since we know that Cos θ/Sin θ = Cot θ and tan θ = 1/Cot θ
⇒ (Cot θ) × Cot θ × (1/Cot θ)
⇒ Cot θ
Simplifying the second term:
[(Sin θ)/(Cos θ)(tan θ)]
⇒ (Sin θ/Cos θ) ×(1/tan θ)
⇒ (tan θ) × (1/tan θ)
⇒ 1
Thus,
[{(Cot θ)(Cos θ)}/Sin θ × tan θ] ÷ [(Sin θ)/(Cos θ)(tan θ)] = (Cot θ) ÷ 1
⇒ Cot θ
Therefore, the simplified expression is Cot θ.
Learn more about trigonometric functions here:
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