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If cos(theta), sin(phi), sin(theta) are in G.P. then roots of x^2 + (2cot(phi))x +1 = 0 are always : (a)equal (b)real (c)imaginary (d)greater than 1

If cos(theta), sin(phi), sin(theta) are in G.P. then roots of x^2 + (2cot(phi))x +1 = 0 are always :


(a)equal


(b)real


(c)imaginary


(d)greater than 1

Grade:12th pass

1 Answers

Saurabh Singh
askIITians Faculty 49 Points
7 years ago
they are in GP so cos theta * sin theta = (sin phi)2
--> 0.5 *sin ( 2*theta) = (sin phi)2
cot phi = cos phi / sin phi
(cot phi)2= (1-(sin phi)2)/(sin phi)2
substitutingthe value of sin phi
(cot phi)2=1
(cot phi)= 1
so our quadratic becomes
x^2 + (2)x +1 = 0
using sri dharacharya
b2-4ac = 4-4*1*1=0
so roots are equal
hence answer is (a)

Thanks & Regards

Saurabh Singh,

askIITians Faculty

B.Tech.

IIT Kanpur

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