Question

If `sin17^(@)=(x)/(y)` then prove that `sec17^(@)-sin73^(@)=(x^(2))/(ysqrt(y^(2)-x^(2)))`

Answer 1

`LHS=sec17^(@)-sin73^(@)`
`(1)/(cos17^(@))-sin(90^(@)-17^(@))`
`=(1)/(cos17^(@))-cos17^(@)=(1-cos^(2)17^(@))/(cos17^(@))`
`=(sin^(2)17^(@))/(sqrt(1-sin^(2)17^(@)))=(((x)/(y))^(2))/(sqrt(1-((x)/(y))^(2)))`
Hence `sec17^(@)-sin73^(@)=(x^(2))/(ysqrt(y^(2)-x^(2)))`