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  • <img alt="\begin{array}{l}{\text { What is the value of }}\ \frac{\cos 15^{\circ}+\sin 15^{\circ}}{\cos 15^{\circ}-\sin 15^{\circ}} \end{array}" src="http://entrancecorner.oncodecogs.com/gif.latex?

\begin{array}{l}{\text { What is the value of }}\ \frac{\cos 15^{\circ}+\sin 15^{\circ}}{\cos 15^{\circ}-\sin 15^{\circ}} \end{array}

Option: 1

\frac{1+\sqrt{3} }{1-\sqrt{3} }


Option: 2

\sqrt{3}


Option: 3

\sqrt{3} -1


Option: 4

1+\sqrt{3}


Answers (1)

best_answer

Trigonometric Ratio for Compound Angles (Part 2)
\\\mathrm{\tan (\alpha+\beta)=\frac{\tan \alpha+\tan \beta}{1-\tan \alpha \tan \beta}}\\\\\mathrm{\tan (\alpha-\beta)=\frac{\tan \alpha-\tan \beta}{1+\tan \alpha \tan \beta}}

 

Now,

\\ { \frac{\cos 15^{\circ}+\sin 15^{\circ}}{\cos 15^{\circ}-\sin 15^{\circ}} \text { (dividing by } \cos 15^{\circ})}\\\\ =\frac{1+\tan 15^{\circ}}{1-\tan 15^{\circ}}\\\\=\frac{\tan 45^{\circ}+\tan 15^{\circ}}{1-\tan 45^{\circ} \tan 15^{\circ}}\\\\=\tan \left(45^{\circ}+15^{\circ}\right)\\\\=\tan 60^{\circ}\\\\=\sqrt{3}

Posted by

Shailly goel

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