Question

If cos A=7/25 and 3π/2<2π, then find the value of cotA/2.

​

Answer 1

Step-by-step explanation:

⟹cot

2

A

=

1−cosθ

1+cosθ

\sf{\implies \cot \dfrac{A}{2} = \sqrt{\dfrac{1 + \dfrac{7}{25} }{1 - \dfrac{7}{25} } }}⟹cot

2

A

=

1−

25

7

1+

25

7

\sf{\implies \cot \dfrac{A}{2} = \sqrt{\dfrac{ \dfrac{25 + 7}{25} }{\dfrac{25 - 7}{25} } }}⟹cot

2

A

=

25

25−7

25

25+7

\sf{\implies \cot \dfrac{A}{2} = \sqrt{\dfrac{ \dfrac{32}{25} }{\dfrac{18}{25} } }}⟹cot

2

A

=

25

18

25

32

\sf{\implies \cot \dfrac{A}{2} = \sqrt{\dfrac{\cancel{32}}{\cancel{18} } }}⟹cot

2

A

=

18

32

\sf{\implies \cot \dfrac{A}{2} = \sqrt{\dfrac{16}{4} }}⟹cot

2

A

=

4

16

\sf{\implies \cot \dfrac{A}{2} = \pm \dfrac{4}{2} }⟹cot

2

A

=±

2

4