Question

if cot theta=root 3,then find the value of cos square theta-sin square theta.

Answer 1

★${\red{\huge{\underline{\underline{\mathtt{Question:-}}}}}}$

If cot∅=√3,then find the value of cos²∅-sin²∅.

${\red{\huge{\underline{\underline{\mathtt{Solution:-}}}}}}$

cot∅ = √3

† We know cot30° = √3 †

→cot∅ = cot30°

→ ∅ = 30°

cos²∅-sin²∅

† Putting the value of ∅ = 30° †

→ cos²30°- sin²30°

↓↓↓

${\purple{\bold{Putting\: the\: values\::-\\cos30=\sqrt{3}/2 \\sin30= 1/2}}}$

→ (√3/2)² - (1/2)²

→ 3/4 - 1/4

→ 2/4

→${\green{\bold{1/2}}}$

★${\red{\huge{\underline{\underline{\mathtt{Answer:-}}}}}}$

Value of (cos²∅ - sin²∅) is ${\purple{\boxed{\bold{1/2}}}}$.

Answer 2

$\huge{ \green{ \mathfrak{ \underline{Question}}}}$

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■☆If $cot \theta= \sqrt{3}$,then find the value of $cos^2 \theta-sin^2 \theta$☆■

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$\huge{ \green{ \mathfrak{ \underline{Answer}}}}$

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$\boxed{\red{\bold{Given:}}}$

$\blue{\implies cot \theta = \sqrt{3}}$

$\implies \theta = coth^{-1} \sqrt{3}$

$\blue{\implies \theta = 30^{\circ}}$

$\boxed{\red{\bold{Put \theta = 30^o}}}$

$cos^2 \theta - sin^2 \theta$

$\implies cos^2 30^o - sin^2 30^o$

$\purple{\implies \left( \displaystyle{\frac{\sqrt{3}}{2}}\right)^2 - \left( \frac{1}{2} \right)^2} \\ (\because \: cos30^o = \frac{\sqrt{3}}{2} \: and \: sin30^o = \displaystyle{\frac{1}{2}})$

$\implies \displaystyle{\frac{3}{4}} - \frac{1}{4}$

$\implies \displaystyle{\frac{2}{4}}$

$\green{\implies \displaystyle{\frac{1}{2}}}$

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