Question

${ {4315 \times \frac{?}{?} }^{2} \times \frac{?}{?} }^{?}$
​

Answer 1

$\huge\mathcal{\mid{\mid{\underline{\purple{Good\: Afternoon\:}}}{\mid{\mid}}}}$

Qᴜᴇsᴛɪᴏɴ ;-

❥︎ If $\bf{\sin\theta\:+\:\cos\theta\:=\:\sqrt{2}\:\cos\theta\:}$, then find the value of $\bf{\tan\theta}$ .

$\huge{\orange{\boxed{\fcolorbox{cyan}{indigo}{\color{lime}ANSWER}}}}$

$\pink\longmapsto\:\:\bf\blue{\sin\theta\:+\:\cos\theta\:=\:\sqrt{2}\:\cos\theta\:}$

$\longmapsto\:\:\sf\pink{\sin\theta\:=\:\sqrt{2}\:\cos\theta\:-\:\cos\theta\:}$

$\longmapsto\:\:\sf\orange{\sin\theta\:=\:\Big(\sqrt{2}\:-\:1\Big)\:\cos\theta\:}$

$\longmapsto\:\:\sf\purple{\dfrac{\sin\theta}{\cos\theta}\:=\:\Big(\sqrt{2}\:-\:1\Big)\:}$

$\Large\bf\pink{We\: know\: that},$

• $\bf\red{\dfrac{\sin\theta}{\cos\theta}\:=\:\tan\theta}$

$\pink\longmapsto\:\:\bf\green{\tan\theta\:=\:\Big(\sqrt{2}\:-\:1\Big)\:}$

Answer 2

Step-by-step explanation:

$⟼sinθ+cosθ= </p><p>2</p><p> </p><p> cosθ</p><p> </p><p> </p><p></p><p>\begin{gathered}\longmapsto\:\:\sf\pink{\sin\theta\:=\:\sqrt{2}\:\cos\theta\:-\:\cos\theta\:} \\ \end{gathered}$

$⟼sinθ= </p><p>2</p><p> </p><p> cosθ−cosθ</p><p> </p><p></p><p>⟼sinθ=( </p><p>2</p><p> </p><p> −1)cosθ$

$⟼ </p><p>cosθ</p><p>sinθ</p><p> </p><p> =( </p><p>2</p><p> </p><p> −1)</p><p>$

$\Large\bf\pink{We\: know\: that},$

$cosθ</p><p>sinθ</p><p> </p><p> =tanθ$

$\begin{gathered}\pink\longmapsto\:\:\bf\green{\tan\theta\:=\:\Big(\sqrt{2}\:-\:1\Big)\:} \\ \end{gathered} </p><p>$

$⟼tanθ=( </p><p>2</p><p> </p><p> −1)$