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A quadratic equation whose roots are cosec square thita and sec square thita can be

A quadratic equation whose roots are cosec square thita and sec square thita can be

Grade:11

2 Answers

Arun
25750 Points
5 years ago
Dear student
 
Equation can be as follows-
 
x² - ( cosec²theta + sec² theta) + cosec ²theta * sec²theta = 0
 
x² - (tan theta + cot theta)² x + 1/sin²theta * cos²theta = 0
 
Regards
Arun (askIITians forum expert)
kkbisht
90 Points
5 years ago
As you know if  \alpha,\beta are the roots of a quadratic equation then the equation formed is :
   x2 -( \alpha +\beta)x + \alpha.\beta=0 => x2 -( cosec2 \theta + sec2\theta)x +cosec2 \theta . sec2\theta=0
 
=> x2 -( 1/sin2\theta + 1/cos2 \theta)x + 1/sin2\theta .1/cos2 \theta=0
=>x2 -( sin2\theta + cos2 \theta). (1/sin2\theta .cos2 \theta)x + 1/sin2\theta .1/cos2 \theta=0
 
x2 -( 1/(sin2\theta .cos2 \theta)x + 1/sin2\theta .1/cos2 \theta=0
=> (sin2\theta .cos2 \theta) x2  -x  +1=0
kkbisht

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