If `0

Explanation

`sin alpha+(tan alpha+cot alpha)+(sec alpha+co sec alpha)=7`
or `(sin alpha+cos alpha)+(1)/(sin alpha cos alpha)+(sin alpha+cos alpha)/(sin alpha cos alpha)=7`
or `(sin alpha+cos alpha)(1+(1)/(sin alpha cos alpha))`
`=7-(1)/(sin alphacos alpha)`
Squaring both sides, we get
or `(1+sin 2alpha)(1+(4)/(sin 2 alpha)+(4)/(sin^(2)2alpha))`
`=49-(28)/(sin 2alpha)+(4)/(sin^(2)2alpha)`
Let `sin 2 alpha=x.` then
`(1+x)(1+(4)/(x)+(4)/(x^(2)))=49-(28)/(x)+(4)/(x^(2))`
or `(1+x)(x^(2)+4x+4)=49x^(2)-28x+4`
or `x^(3)-44x^(2)+36x=0`
or `x^(2)-44x+36=0 ("as" x=sin 2 alpha ne 0)`