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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

If sec θ + tan θ = sqrt(3), complete the activity to find the value of sec θ – tan θ. Activity: square = 1 + tan^2θ ...[Fundamental trigonometric identity] square – tan^2θ = 1

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प्रश्न

If `sec θ + tan θ = sqrt(3)`, complete the activity to find the value of sec θ – tan θ.

Activity:

`square = 1 + tan^2θ`   ...[Fundamental trigonometric identity]

`square - tan^2θ = 1`

`(sec θ + tan θ) . (sec θ - tan θ) = square`

`sqrt(3)  . (sec θ - tan θ) = 1`

`(sec θ - tan θ) = square`

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बेरीज
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उत्तर

\[\boxed{\text{sec}^2θ} = 1 + \text{tan}^2θ\]   ...[Fundamental trigonometric identity]

\[\boxed{\text{sec}^2θ} - \text{tan}^2θ = 1\]

(sec θ + tan θ) . (sec θ – tan θ) = \[\boxed{1}\]

`sqrt(3)  . (sectheta - tan theta)` = 1

\[(\text{sec} θ - \text{tan} θ) = \boxed{\frac{1}{\sqrt3}}\] 

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पाठ 6: Trigonometry - Q.2 (A)

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