Question

If tan tange =1, then find sec tange ​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf tan\theta =1$

• This the value of tan 45°
• means :-

$\sf tan 45{}^{\circ}= 1\\ \\ \sf\implies \theta =45{}^{\circ}$

• we have to find the value of

• $\sf sec\theta$

• Means sec 45°

$\sf\implies sec \theta =\dfrac{1}{cos\:\theta}\\ \\ \sf\implies\:\: or\: \theta=45{}^{\circ}\\ \\ \sf\implies sec45{}^{\circ}=\dfrac{1}{cos45{}^{\circ}} \\ \\ \sf{\blue{cos 45{}^{\circ}=\dfrac{1}{\sqrt{2}}}}\\ \\ \sf\implies sec 45{}^{\circ}=\dfrac{1}{\dfrac{1}{\sqrt{2}}}\\ \\ \sf\implies sec\: 45{}^{\circ}= \sqrt{2}$

• So the value of

$\boxed{\sf{sec\:\theta= \sqrt{2}}}$

Answer 2

$\huge\underline\mathrm{Question-}$

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If $\sf{Tan\theta=1}$

Find $\sf{Sec\theta}$

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$\huge\underline\mathrm{Answer-}$

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$\huge{\boxed{\mathrm{\red{Sec\theta=\sqrt2}}}}$

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$\huge\underline\mathrm{Solution-}$

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It is given that, $\sf{Tan\theta=1}$

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And we know that, Tan45° = 1,

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so we can say that the value of $\theta$ is 45°.

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Now, we have to find the value of $\sf{Sec\theta}$,

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Also, $\sf{Sec\theta}$ = $\sf{\dfrac{1}{Cos\theta}}$

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And the value of $\sf{Cos45°}$ is $\sf{\dfrac{1}{\sqrt2}}$

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$\implies$ Sec45° = $\dfrac{1}{ \frac{1}{ \sqrt{2} } }$

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By reciprocate, we get,

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Sec45° = √2

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$\huge{\boxed{\mathrm{\red{\therefore\:Sec\theta=\sqrt2}}}}$