Question

1- cos²45°/1+cos² 45°

Answer 1

Question :-

$\frac{1 - \cos {}^{2} 45 {}^{0} }{1 + \cos {}^{2} 45 {}^{0} }$

Solution :-

$\frac{1 - \cos {}^{2} 45 {}^{0} }{1 + \cos {}^{2} 45 {}^{0} }$

We know that

$\cos(45 {}^{0} ) = \frac{1}{ \sqrt{2} }$

Now put this value

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

Now solve this

$\frac{1 - \frac{1}{2} }{1 + \frac{1}{2} } = \frac{ \frac{2 - 1}{2} }{ \frac{2 + 1}{2} } \\ \\ \frac{ \frac{1}{2} }{ \frac{3}{2} } = \frac{1}{2} \times \frac{2}{3} \\ \\ \\= ( \frac{1}{3}) \: \: \: \: \: \: \: \: \: \: Answer$

Hint:-

• $( \sqrt{n} ) {}^{2} = n$

• Example : $( \sqrt{7} ) {}^{2} = 7$

Answer 2

${\bold{\blue{\boxed{\bf{Question}}}}}$

$\sf \dfrac{1-cos^2 45}{1 + cos^2 45}$

${\bold{\blue{\boxed{\bf{Solution}}}}}$

$\sf \implies\dfrac{1-cos^2 45}{1 + cos^2 45}$

${\bold{\blue{\boxed{\bf{cos 45 = \dfrac{1}{\sqrt 2}}}}}}$

$\sf \implies\dfrac{1-(\dfrac{1}{\sqrt 2})^2}{1 +( \dfrac{1}{\sqrt 2})^2}$

$\sf \implies\dfrac{\dfrac{ 2 -1}{2}}{ \dfrac{2 + 1}{ 2}}$

$\sf \implies{\dfrac{1}{2}} \times{ \dfrac{ 2}{ 3}}$

$\sf\implies\dfrac{ 1}{ 3}$

${\bold{\blue{\boxed{\bf{Answer = \dfrac{1}{3}}}}}}$

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