Question

sin15/cos15 x tan 45

Answer 1

I hope my helping hands will help you my friend....

Answer 2

Answer:

Value of given expression is 2 - √3

Step-by-step explanation:

Given Expression: $\frac{sin\,15^{\circ}}{cos15^{\circ}}\times tan\,45^{\circ}$

To find: Value of given Expression

Identity used,

$tan(A+B)=\frac{tan\,A+tan\,B}{1+tan\,A\:tan\,B}$

$tan\,x=\frac{sin\,x}{cos\,x}$

$tan\,45^{\circ}=1\;\:and\:\:tan\,30^{\circ}=\frac{1}{\sqrt{3}}$

Consider,

$\frac{sin\,15^{\circ}}{cos15^{\circ}}\times tan\,45^{\circ}$

$\implies tan\,15^{\circ}\times1$

$\implies tan\,(45^{\circ}-30^{\circ})$

$\implies \frac{tan\,45^{\circ}-tan\,30^{\circ}}{1+tan\,45^{\circ}\:tan\,30^{\circ}}$

$\implies \frac{1-\frac{1}{\sqrt{3}}}{1+1\:\frac{1}{\sqrt{3}}}$

$\implies \frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\:\frac{\sqrt{3}+1}{\sqrt{3}}}$

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

$\implies \frac{\sqrt{3}-1}{\sqrt{3}+1}\times\frac{\sqrt{3}-1}{\sqrt{3}-1}$

$\implies \frac{(\sqrt{3}-1)^2}{(\sqrt{3})^2-1^2}$

$\implies \frac{3+1-2\sqrt{3}}{3-1}$

$\implies \frac{4-2\sqrt{3}}{2}$

$\implies2-\sqrt{3}$