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Sagot :
The value for given trigonometric functions are csc 30° = 2, cot 60° = √3/3, cos 30 ° = √3/2, and cot 30° = √3.
A branch of mathematics called trigonometry examines correlations between side lengths and angles of the triangle. Trigonometric Identities are equality conditions that apply to all values of the variables in the equation and which require trigonometry functions.
Given, sin 30° = 1/2 and tan 30° = √3/3.
The formula for csc or cosec x = 1/sinx.
Then,
[tex]\begin{aligned}\csc 30^{\circ} &=\frac{1}{\frac{1}{2}}\\&=2\end{aligned}[/tex]
The formula for cot θ = tan(90°- θ)
Then,
[tex]\begin{aligned}\cot 60^{\circ} & = \tan(90^{\circ}-60^{\circ}) \\&= \tan 30^{\circ}\\&=\frac{\sqrt{3}}{3}\end{aligned}[/tex]
The formula for cos θ = sin θ/tan θ.
Then,
[tex]\begin{aligned}\cos 30^{\circ} &= \frac{\sin 30^{\circ}}{\tan 30^{\circ}}\\&= \frac{\frac{1}{2}}{\frac{\sqrt{3}}{3}}\\&=\frac{3}{2\sqrt3}\times \frac{\sqrt3}{\sqrt3}\\&=\frac{\sqrt3}{2} \end{aligned}[/tex]
The formula for cot θ = 1/tan θ.
Then,
[tex]\begin{aligned}\cot 30^{\circ}&=\frac{1}{\tan30^{\circ}}\\&=\frac{1}{\frac{\sqrt3}{3}}\\&=\frac{3}{\sqrt3}\times\frac{\sqrt3}{\sqrt3}\\&=\sqrt{3}\end{aligned}[/tex]
Therefore, the answers are 2, √3/3, √3/2, and √3.
To know more about trigonometric identities:
https://brainly.com/question/25024376
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