Question

If `sin10theta=cos8thetaand10theta` is a positive acute angle, then find the value of `tan9theta`.

Answer 1

Given that `sin10theta=cos8thetaand10theta` is acute.
`:.sin10theta=sin(90^(@)-8theta)`
`implies10theta=90^(@)-8theta`
`implies10theta+8theta=90^(@)`
`implies18theta=90^(@)`
`impliestheta=(90^(@))/(18)`
`impliestheta=5^(@)`
`implies9theta=9xx5^(@)=45^(@)`
`impliestan9theta=tan45^(@)`
`impliestan9theta=1`
Hence the value of `tan9theta=1`