Question

If tan ø =1 then, find the value of sinø + cos ø/secø+ cosec ø​

Answer 1

$\huge \underline{\underline{\tt Correct \: Question :}}$

If tanθ = 1, find value of :

• $\sf \dfrac{sin\theta + cos\theta}{sec \theta + cosec\theta}$

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$\huge \underline{\underline{\tt Answer :}}$

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Given :

• tanθ = 1

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To Find :

• $\sf \dfrac{sin\theta + cos\theta}{sec \theta + cosec\theta} = ?$

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Solution :

We are given :

tanθ = 1

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We also know that :

tan45° = 1

$\sf : \implies tan\theta = tan45^{\circ}$

$\sf : \implies \theta = 45^{\circ}$

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Now, we have to find :

$\sf \dfrac{sin\theta + cos\theta}{sec \theta + cosec\theta}$

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By, filling value of θ = 45° :

$\sf : \implies \dfrac{sin45^{\circ} + cos45^{\circ}}{sec 45^{\circ} + cosec45^{\circ}}$

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Now, we have :

• sin45° = $\sf \dfrac{1}{\sqrt{2}}$

• cos45° = $\sf \dfrac{1}{\sqrt{2}}$

• sec45° = $\sf \sqrt{2}$

• cosec45° = $\sf \sqrt{2}$

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By filling values :

$\sf : \implies \dfrac{\dfrac{1}{\sqrt{2}} + \dfrac{1}{\sqrt{2}}}{\sqrt{2} + \sqrt{2}}$

$\sf : \implies \dfrac{\dfrac{1+1}{\sqrt{2}}}{2\sqrt{2}}$

$\sf : \implies \dfrac{\dfrac{2}{\sqrt{2}}}{\dfrac{2\sqrt{2}}{1}}$

$\sf : \implies \dfrac{2}{\sqrt{2}} \times \dfrac{1}{2\sqrt{2}}$

$\sf : \implies \dfrac{2}{\sqrt{2} \times 2\sqrt{2}}$

$\sf : \implies \dfrac{2}{2 (\sqrt{2})^{2}}$

$\sf : \implies \dfrac{2}{2 \times 2}$

$\sf : \implies \cancel{\dfrac{2}{4}}$

$\sf : \implies \dfrac{1}{2}$

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$\bf \therefore \: value \: of \: \dfrac{sin\theta + cos\theta}{sec \theta + cosec\theta} = \dfrac{1}{2}$