1.

उचित अबुवासिकस्थान पर अस्वार यालगाकर उसे रिस्तकीप्पगड पर फिर सेस्थाबालिखे।बाधवापाडाभिखममातुरत​

Answer»

align="absmiddle" ALT="\bf{To\:PROVE :}\:\sf\dfrac{cos\theta+1-sin\theta}{cos\theta-1+sin\theta}=\dfrac{1+sin\theta}{cos\theta}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5Cbf%7BTo%5C%3AProve%20%3A%7D%5C%3A%5Csf%5Cdfrac%7Bcos%5Ctheta%2B1-sin%5Ctheta%7D%7Bcos%5Ctheta-1%2Bsin%5Ctheta%7D%3D%5Cdfrac%7B1%2Bsin%5Ctheta%7D%7Bcos%5Ctheta%7D" title="\bf{To\:Prove :}\:\sf\dfrac{cos\theta+1-sin\theta}{cos\theta-1+sin\theta}=\dfrac{1+sin\theta}{cos\theta}">

\bf{Proof :}

:\implies\sf\ \dfrac{ \dfrac{(cos\theta+1-sin\theta)}{sin\theta}}{ \dfrac{(cos\theta-1+sin\theta)}{sin\theta}}\\\\{\scriptsize\qquad\bf{\dag}\:\:\tt{Dividing\ By\ sin\theta}}\\ \\ :\implies\sf \ \dfrac{cot\theta+csc\theta-1}{cot\theta-csc\theta+1}\\ \\ \\ :\implies\sf \ \dfrac{cot\theta+csc\theta-\big(csc^2\theta-cot^2\theta\big)}{cot\theta-csc\theta+1}\\ \\ {\scriptsize\qquad\bf{\dag}\:\:\tt{1= csc^2\theta-cot^2\theta}}

⠀

:\implies\sf\ \dfrac{csc\theta+cot\theta-\big(csc\theta+cot\theta\big)\big(csc\theta-cos\theta \big)}{cot\theta-csc\theta+1}\\ \\ {\scriptsize\qquad\bf{\dag}\:\:\tt{\ a^2-b^2=(a+b)(a-b)}} \\ \\ :\implies\sf \ \dfrac{csc\theta+cos\theta [1-(csc\theta-cot\theta)]}{cot\theta-csc\theta+1}\\ \\ \\ :\implies\sf \ \dfrac{csc\theta+cot\theta \bcancel{[1-csc\theta+cot\theta]}}{\bcancel{cot\theta-csc\theta+1}}\\ \\ \\ :\implies\sf\ csc\theta+cot\theta\\ \\ \\ :\implies\sf \ \dfrac{1}{sin\theta}+\dfrac{cos\theta}{sin\theta}\\ \\ \\ :\implies\underline{\boxed{\sf \dfrac{1+cos\theta}{sin\theta}}}

⤵️

Answer:

Let the Numerator be n and Denominator be (n - 5) of the Fraction.

If 9 is subtracted from the numerator and 1 is added to the denominator, the number becomes 7/2

\underline{\bigstar\:\textsf{According to the given Question :}}

:\implies\sf \dfrac{Numerator-9}{Denominator+1}=\dfrac{7}{2}\\\\\\:\implies\sf \dfrac{n-9}{(n - 5)+1}=\dfrac{7}{2}\\\\\\:\implies\sf \dfrac{n-9}{n - 4}=\dfrac{7}{2}\\\\\\:\implies\sf 2(n - 9) = 7(n - 4)\\\\\\:\implies\sf 2n - 18 = 7n - 28\\\\\\:\implies\sf 28 - 18 = 7n - 2n\\\\\\:\implies\sf 10 = 5n\\\\\\:\implies\sf \dfrac{10}{5} = n\\\\\\:\implies\sf n = 2

⠀

\dag\:\underline{\boxed{\sf Original\:Fraction=\dfrac{n}{n-5} = \dfrac{2}{ - \:3} = \dfrac{ - \:2}{3} }}


Discussion

No Comment Found

Related InterviewSolutions