Question

Cosectheta-cottheta=1/4 find value of cosectheta +cottheta

Answer 1

According to question,

                          Cosec theta - Cot theta = 1/4

Expanding it into cos and sin

                         1/Sin theta - Cos theta / Sin theta = 1/4

taking the denominator,

W get, 
                           (1 - Cos theta) / Sin theta = 1/4

Now doing the reciprocal on both the sides

We get,

                         (Sin theta) / (1-Cos theta)  = 4

Multiplying the numerator and the denominator of LHS with (1 +Cos theta)

 we get,

                 Sin theta * (1 + Cos theta) / (1 - Cos theta) * (1 + Cos theta) = 4

We know,
              (a+b) (a-b)  = a^2 -b^2

So (1 + Cos theta) (1- Cos theta) = 1- Cos^2 theta

                                                     =  Sin^ theta

Thus putting this term in the above equation,
 
                  Sin theta * (1 + Cos theta) / Sin^2 theta = 4

                                    (1 + Cos theta) / Sin theta = 4

Separating the denominator,
                           1/Sin theta + Cos theta / Sin theta = 4
                        Cosec theta +  Cot theta = 4
Thus, the value of Cosec theta + Cot theta is 4

I hope u get it.

Mark Brainliest!! BRO!!

Answer 2

hey I m refering theta to be a

so we know cosec^2a-cot^2a=1
so(cosec a+cot a )(cosec a -cot a )=1
now cosec a +cot a (1/4)=1
so cosec a + cot a =4