Let yarctanx10 Write cscy as an expression in terms of xSolu

Let y=arctan(x/10). Write csc(y) as an expression in terms of x.

Solution

given y=arctan(x_/10)

=> tan(y)=(x_/10)

tan(y)=opposite side _{/adjacent side}

opposite side =x ,adjacent side =10

hypotenuse²=opposite side²+adjacent side²

hypotenuse²=x²+10²

hypotenuse²=x²+100

hypotenuse=(x²+100)

csc(y)=hypotenuse_{/opposite side}

csc(y)=((x²+100))_/x