Question

1-sin^45 /1+sin^45=?

Answer 1

1-Sin45°/ 1+ sin45°

1-1/✓2/ 1+ 1/✓2

= ✓2-1 / ✓2+1

= ✓2-1/✓2+1 × ✓2-1/✓21-1 = (✓2-1)²/ (✓2)²-(1)²

= 2 - 2✓2+1 / 2-1 = 3-2✓2/1 = 3-2✓2

Answer 2

Solution:

______________________________________________________________

Given & To find:

$\frac{1- sin45}{1+ sin 45}$

_____________________________________________________________

As we know,

sin 45° =$\frac{1}{ \sqrt{2} }$

_________________________________

so,

$\frac{1-sin 45}{1+ sin 45}$

=> $\frac{1 - \frac{1}{ \sqrt{2} } }{ \frac{1}{ \sqrt{2} + 1} }$

=> ($\frac{ \sqrt{2} - 1 }{ \sqrt{2} +1}$)

By taking conjugate,

we get,

=> $\frac{ \sqrt{2}-1 }{ \sqrt{2}+1 } ( \frac{ \sqrt{2}-1 }{ \sqrt{2} - 1 } )$

=>$\frac{( \sqrt{2} - 1 )^2}{ (\sqrt{2})^2 -(1)^2 }$

=> $\frac{2-2 \sqrt{2} +1}{2-1}$

=> $\frac{3 - 2 \sqrt{2} }{1}$


=> ∴ $3 - 2 \sqrt{2}$

____________________________________________________________
 

                                 Hope it Helps!!