English, asked by nandita58, 1 year ago

if ( cosecA+sinA / cosecA-sinA ) = 5/2
so, sinA=?​

Answers

Answered by Anonymous
7

Given \:  \:  \: Question \:  \: Is \:  \:  \\  \\  \frac{ \csc(x)  +  \sin(x) }{ \csc(x)  -  \sin(x) }  =  \frac{5}{2}  \\  \\  \frac{ \frac{1}{ \sin(x) }  +  \sin(x) }{ \frac{1}{ \sin(x) } -  \sin(x)  }  =  \frac{5}{2}  \\  \\  \frac{ \frac{1 +  \sin {}^{2} (x) }{ \sin(x) } }{ \frac{1 -  \sin {}^{2} (x) }{ \sin(x) } }  =  \frac{5}{2}  \\  \\  \frac{1 +  \sin {}^{2} (x) }{1 -  \sin {}^{2} (x) }  =  \frac{5}{2}  \\  \\ 2 + 2 \sin {}^{2} (x)  = 5 - 5 \sin {}^{2} (x)  \\  \\ 2 - 5 =  - 5 \sin {}^{2} (x)  - 2 \sin {}^{2} (x)  \\  \\  - 3 =  - 7 \sin {}^{2} (x)  \\  \\ 3 = 7 \sin {}^{2} (x)  \\  \\  \sin {}^{2} (x)  =  \frac{3}{7}  \\  \\ taking \: square \: root \: on \: both \: sides \: we \: have \\  \\  \sqrt{ \sin {}^{2} (x) }  =  \sqrt{ \frac{3}{7} }  \\  \\  | \sin(x) |  =  \sqrt{ \frac{3}{7} }  \\  \\  \sin  (x)  =  \sqrt{ \frac{3}{7} }  \:  \:  \:  \: or \:  \:  \:  \:  \:  \sin(x)  =  -  \sqrt{ \frac{3}{7} }  \\  \\ NOTE \\  \\ where \: x \:  = A \:  \:  \:  \\  \\  \csc(x)  \:  =  \frac{1}{ \sin(x) }


nandita58: but the answer is 1/2
nandita58: I did the same process.
nandita58: My answers are same which you did.
Anonymous: okay:-)
Answered by anu24239
3

\huge\mathfrak\red{Answer}

 \frac{ \csc \alpha  +  \sin \alpha  }{ \csc \alpha  -  \sin \alpha   }  =  \frac{5}{2}  \\  \\ apply \: componendo \: and \: dividendo \\  \\  \frac{ \csc \alpha  +  \sin \alpha  +  (\csc \alpha  -  \sin \alpha )   }{ \csc \alpha  +  \sin \alpha  - ( \csc \alpha  -  \sin \alpha )}  =  \frac{5 + 2}{5 - 2}  \\  \\   \frac{2 \csc \alpha  }{2 \sin \alpha }  =  \frac{7}{3}  \\  \\  \frac{1}{ {sin}^{2}  \alpha } =   \frac{7}{3}  \\   \\  {sin}^{2}  \alpha  =  \frac{3}{7}  \\  \\  \sin \alpha  =  \frac{ \sqrt{3} }{ \sqrt{7} }  \\  \\  \alpha  =  {sin}^{ - 1}  \sqrt{ \frac{3}{7} }

WHAT IS COMPONENDO AND DIVIDENDO?

suppose \: a \: fraction \:  \\   \\ \frac{a}{b}   \: which \: is \: equal \: to \: another \: fraction \\  \frac{c}{d}  \\  \\  \frac{a}{b}  =  \frac{c}{d}  \\   \\ than \: after \: componendo \: and \\ dividendo \\  \\  \frac{a + b}{a - b}  =  \frac{c + d}{c - d}

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