Question

if cosA=7/25 and 3π\2 is less than A is less than 2π,value of cotA/2​

Answer 1

Answer :-

Given :-

• 3π/2<A<2π

• 3π/2 =270° and 2π. =360°

• So A will lie in 4th quadrant.

• In 4th quadrant cot functions as negative.

Solution :-

$\sf{\implies \cot \dfrac{A}{2} = \sqrt{\dfrac{1 + \cos \theta }{1 - \cos \theta } }}$

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

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

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

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

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

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

As it given that the angle lines in the the fourth quadrant and in fourth quadrant the function of cot is negative

• $\sf{\implies \cot \dfrac{A}{2} = - \dfrac{4}{2} }}$

Answer 2

Answer:

Step-by-step explanation: