JEE MAIN - Mathematics (2007 - No. 5)
If sin-1$$\left( {{x \over 5}} \right)$$ + cosec-1$$\left( {{5 \over 4}} \right)$$ = $${\pi \over 2}$$, then the value of x is :
4
5
1
3
स्पष्टीकरण
Given sin-1$$\left( {{x \over 5}} \right)$$ + cosec-1$$\left( {{5 \over 4}} \right)$$ = $${\pi \over 2}$$
$$ \Rightarrow $$ sin-1$$\left( {{x \over 5}} \right)$$ + sin-1$$\left( {{4 \over 5}} \right)$$ = $${\pi \over 2}$$
$$ \Rightarrow $$ sin-1$$\left( {{x \over 5}} \right)$$ = $${\pi \over 2}$$ - sin-1$$\left( {{4 \over 5}} \right)$$
$$ \Rightarrow $$ sin-1$$\left( {{x \over 5}} \right)$$ = cos-1$$\left( {{4 \over 5}} \right)$$
$$ \Rightarrow $$ $${x \over 5}$$ = sin(cos-1$$ {{4 \over 5}}$$)
$$ \Rightarrow $$ $${x \over 5}$$ = sin(sin-1$$ {{3 \over 5}}$$)
$$ \Rightarrow $$ $${x \over 5}$$ = $${3 \over 5}$$
$$ \Rightarrow $$ x = 3
$$ \Rightarrow $$ sin-1$$\left( {{x \over 5}} \right)$$ + sin-1$$\left( {{4 \over 5}} \right)$$ = $${\pi \over 2}$$
$$ \Rightarrow $$ sin-1$$\left( {{x \over 5}} \right)$$ = $${\pi \over 2}$$ - sin-1$$\left( {{4 \over 5}} \right)$$
$$ \Rightarrow $$ sin-1$$\left( {{x \over 5}} \right)$$ = cos-1$$\left( {{4 \over 5}} \right)$$
$$ \Rightarrow $$ $${x \over 5}$$ = sin(cos-1$$ {{4 \over 5}}$$)
$$ \Rightarrow $$ $${x \over 5}$$ = sin(sin-1$$ {{3 \over 5}}$$)
$$ \Rightarrow $$ $${x \over 5}$$ = $${3 \over 5}$$
$$ \Rightarrow $$ x = 3