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

Arun
23513 Points

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
one year ago
kkbisht
90 Points

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 $\theta$x -x  +1=0
kkbisht
one year ago
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