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If sin =p, where | p | 1 then quadratic equation whose roots

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If $s in α = p$ , where $∣ p ∣ ⩽ 1$ then quadratic equation whose roots are $tan \frac{α}{2}$ and $cot \frac{α}{2}$ is

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Camila Discussed

s in α = p

, where

∣ p ∣ ⩽ 1

then quadratic equation whose roots are

tan \frac{α}{2}

and

cot \frac{α}{2}

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Consider that A quadratic equation

a x^{2} + b x + c = 0

and roots of this equation is

tan \frac{α}{2} an d cot \frac{α}{2}

Since we know that if

p an d q

and root of a quadratic equation thenn equation is

x^{2} - (p + q) x + pq = 0

So our equation is

x^{2} - (tan \frac{α}{2} + cot \frac{α}{2}) x + tan \frac{α}{2} cot \frac{α}{2} = 0

x^{2} - ⎝ ⎛ \frac{sin \frac{α}{2}}{cos \frac{α}{2}} + \frac{cos \frac{α}{2}}{sin \frac{α}{2}} ⎠ ⎞ x + 1 = 0

x^{2} - ⎝ ⎛ \frac{sin ^{2} \frac{α}{2} + cos ^{2} \frac{α}{2}}{sin \frac{α}{2} cos \frac{α}{2}} ⎠ ⎞ x + 1 = 0

x^{2} - ⎝ ⎛ \frac{1}{sin \frac{α}{2} cos \frac{α}{2}} ⎠ ⎞ x + 1 = 0

x^{2} - 2 \times \frac{1}{sin α} x + 1 = 0

[∵ sin α = p]

x^{2} - \frac{2}{p} x + 1 = 0

Which is our required quadratic equation.

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Question Text	If $s in α = p$ , where $∣ p ∣ ⩽ 1$ then quadratic equation whose roots are $tan \frac{α}{2}$ and $cot \frac{α}{2}$ is
Answer Type	Text solution:1
Upvotes	150