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Mathematics

Find the value of cot x.

Find the value of cot x. Solution of Right Triangles, Concise Mathematics Solutions ICSE Class 9.

Trigonometric Identities

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Answer

Find the value of cot x. Solution of Right Triangles, Concise Mathematics Solutions ICSE Class 9.

In Δ ABC, according to Pythagoras theorem,

⇒ AC2 = BC2 + AB2 (∵ AC is hypotenuse)

⇒ 22 = BC2 + (3\sqrt3)2

⇒ 4 = BC2 + 3

⇒ BC2 = 4 - 3

⇒ BC2 = 1

⇒ BC = 1\sqrt1

⇒ BC = 1

cot x=BasePerpendicularcot x=CBABcot x=13\text{cot x} = \dfrac{Base}{Perpendicular}\\[1em] \text{cot x} = \dfrac{CB}{AB}\\[1em] \text{cot x} = \dfrac{1}{\sqrt3}

Hence, cot x = 13\dfrac{1}{\sqrt3}.

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