Question

formulas for trigonometry ​

Answer 1

Answer:

Formulas for Trigonometry are :

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${\sf{\bigstar \ \ sin \theta = {\dfrac{Perpendicular}{Hypotenuse}}}}$

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${\sf{\bigstar \ \ cosec \theta = {\dfrac{Hypotenuse}{Perpendicular}}}}$

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${\sf{\bigstar \ \ cos \theta = {\dfrac{Base}{Hypotenuse}}}}$

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${\sf{\bigstar \ \ sec \theta = {\dfrac{Hypotenuse}{Base}}}}$

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${\sf{\bigstar \ \ tan \theta = {\dfrac{Base}{Perpendicular}}}}$

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${\sf{\bigstar \ \ cot \theta = {\dfrac{Perpendicular}{Base}}}}$

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${\sf{\bigstar \ \ tan \theta = {\dfrac{sin \theta}{cos \theta}}}}$

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${\sf{\bigstar \ \ cot \theta = {\dfrac{cos \theta}{sin \theta}}}}$

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${\sf{\bigstar \ \ sin^2 \theta + cos^2 \theta = 1}}$

$\implies{\sf{sin^2 \theta = 1 - cos^2 \theta}}$

$\implies{\sf{cos^2 \theta = 1 - sin^2 \theta}}$

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${\sf{\bigstar \ \ 1 + tan^2 \theta = cot^2 \theta}}$

$\implies{\sf{1 = cot^2 \theta - tan^2 \theta}}$

$\implies{\sf{tan^2 \theta = cot^2 \theta - 1}}$

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${\sf{\bigstar \ \ 1 + cot^2 \theta = cosec^2 \theta}}$

$\implies{\sf{1 = cosec^2 \theta - cot^2 \theta}}$

$\implies{\sf{cot^2 \theta = cosec^2 \theta - 1}}$

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Answer 2

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-:$\:\:Formulas\:For\:Trigonometry\:\:$:-

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⭐ sin⊖ = $\frac{Perpendicular}{Hypotenuse}$

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⭐ cosec⊖ = $\frac{Hypotenuse}{Perpendicular}$

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⭐ cos⊖ = $\frac{Base}{Hypotenuse}$

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⭐ sec⊖ = $\frac{Hypotenuse}{Base}$

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⭐ tan⊖ = $\frac{Base}{Perpendicular}$

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⭐ cot⊖ = $\frac{Perpendicular}{Base}$

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⭐ tan⊖ = $\frac{sin⊖}{cos⊖}$

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⭐ cot⊖ = $\frac{cos⊖}{sin⊖}$

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⭐ sin²⊖ + cos²⊖ = 1

$\implies$ sin²⊖ = 1 - cos²⊖

$\implies$ cos²⊖ = 1 - sin²⊖

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⭐ 1 + tan²⊖ = cos²⊖

$\implies$ 1 = 1 - cot²⊖ - tan²⊖

$\implies$ tan²⊖ = cot²⊖ -1

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⭐ 1 + cot²⊖ = cosec²⊖

$\implies$ 1 = cosec²⊖ - cot²⊖

$\implies$ cot²⊖ = cosec²⊖ -1

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