Trigonometry> A quadratic equation whose roots are cose...

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

Ashidh , 7 Years ago

Grade 11

2 Answers

Arun

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)

Last Activity: 7 Years ago

kkbisht

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

Last Activity: 7 Years ago

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Trigonometry> A quadratic equation whose roots are cose...

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

Ashidh , 7 Years ago

Arun

kkbisht

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