UPSC NDA Math Model Paper 9

As we know that, cot x = cos x / sin x
⇒cot(22

1

2°

)=

cos(22 1 2 °)

sin(22 1 2 °)

As we know that, sin‌

A

2

=±√

1−cos‌A

2

⇒sin(

45°

2

)=±√

1−cos(45°)

2

As we know that, 0° < A / 2 < 90° where all trigonometric ratios are positive.
⇒sin(

45°

2

)=√

√2−1

2√2

........(1)
As we know that, cos‌

A

2

=±√

1+cos‌A

2

⇒cos(

45°

2

)=±√

1+cos(45°)

2

.........(2)
As we know that, 0° < A / 2 < 90° where all trigonometric ratio’s are positive.
⇒cos(

45°

2

)=√

√2+1

2√2

So, from equation (1) and (2), we get
⇒cot(22

1

2°

)=

√ √2+1 2√2

√ √2−1 2√2

=1+√2