Math, asked by sahibarsh321, 4 days ago

if x sinA = 5 and 7 cosecA = 6 SecA then find the valus of x​

Answers

Answered by rajat2181
3

 \sin(a)  =  \frac{5}{x}  \\

7 \cosec(a)  = 6 \sec(a)  \\   \frac{\cosec(a) }{ \sec(a) } =  \frac{6}{7}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:

 \frac{ \cosec(a) }{ \sec(a) }  =  \cot(a) =  \frac{6}{7}   \\

Using Identity:

1 +  { \cot}^{2} (a) =  \cosec {}^{2} (a)

1 +  {( \frac{6}{7} )}^{2}  =  \frac{1}{ \sin{ }^{2} (a) }  \\

1 +  \frac{36}{49}  =  \frac{1}{ (\frac{5}{x} ) {}^{2} }  \\

 \frac{49 + 36}{49}  =  \frac{x {}^{2} }{25}  \\

 \frac{85}{49}  \times 25 =  {x}^{2}  \\

x =  \sqrt{ \frac{85 \times 25}{49} }  \\

x =  \frac{5}{7}  \sqrt{85}  \\

Answered by Manmohan04
1

Given,

\[\begin{array}{l}x\sin A = 5 -  -  -  - \left( 1 \right)\\7\cos ecA = 6\sec A -  -  -  - \left( 2 \right)\end{array}\]

Solution,

Consider the equation 2,

\[\begin{array}{l}7\cos ecA = 6\sec A\\ \Rightarrow \frac{7}{{\sin A}} = \frac{6}{{\cos A}}\\ \Rightarrow \tan A = \frac{7}{6}\end{array}\]

Calculate the value of \[\sin A\],

\[\begin{array}{l}\sin A = \frac{7}{{\sqrt {{7^2} + {6^2}} }}\\ \Rightarrow \sin A = \frac{7}{{\sqrt {85} }}\end{array}\]

Put this value in equation 1,

\[x\sin A = 5\]

\[ \Rightarrow x \times \frac{7}{{\sqrt {85} }} = 5\]

\[ \Rightarrow x = \frac{{5\sqrt {85} }}{7}\]

Hence the value of x is \[\frac{{5\sqrt {85} }}{7}\]

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