Question

if cosec theta -cot theta = k then find cosec theta +cot theta =?​

Answer 1

Answer:

cosec theta + cot theta = 1 / k

Step-by-step explanation:

I used x instead of theta was facing problem adding online

cosecx + cot x = k .....................................................(given)

divide & multiply LHS with cosecx - cot x

(cosecx + cot x) (cosecx - cot x) / (cosecx - cot x) = k

$(cosec^{2} x - cot^{2} x) / cosecx + cot x = k$

$(cosec^{2} x - cot^{2} x) / k = cosecx + cot x$ -------------------- equation 1

Now solve

$(cosec^{2} x - cot^{2} x)$

= $\frac{1}{sin^{2} x}$ - $\frac{cos^{2} x}{sin^{2} x}$

= $\frac{1- sin^{2} x}{cos^{2} x}$

= $\frac{cos^{2} x}{cos^{2} x}$   (used $sin^{2} x + cos^{2} x = 1$)

= 1

Now use equation 1

$(cosec^{2} x - cot^{2} x) / k = cosecx + cot x$

1/ k = $cosecx + cot x$