If sin-1[( x 5 )] + cosec-1[( 5 4 )] = [ 2], then the value of x is :

Question

If sin-1$$\left( {{x \over 5}} \right)$$ + cosec-1$$\left( {{5 \over 4}} \right)$$ = $${\pi  \over 2}$$, then the value of x is :

Accepted Answer

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

Solutions · 1