Question

Cos135°-cos120°\cos135+COS120°

Answer 1

Step-by-step explanation:

(cos(135°)-cos(120°))/cos(135°)+cos(120°)

=>

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

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

Rationalise the denominator

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

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

Hope it helps you.

Answer 2

Step-by-step explanation:

cos(135°)-cos(120°))/cos(135°)+cos(120°)

=>

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

2

−1

−

2

1

2

−1

−(

2

−1

)

=>

−

2

1

−

2

1

2

−1

+

2

1

=>

2

−(

2

+1)

2

1−

2

=>

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

−(

2

+1)

−(

2

−1)

=>

2

+1

2

−1

Rationalise the denominator

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

(

2

+1)(

2

−1)

(

2

−1)

2

=>(

2

−1)

2

=>

2 + 1 - 2 \sqrt{2} = > 3 - 2 \sqrt{2}2+1−2

2

=>3−2

2