[tex]\bf \textit{Cofunction Identities}
\\ \quad \\
\boxed{sin\left(\frac{\pi}{2}-{{ \theta}}\right)=cos({{ \theta}})}\qquad
cos\left(\frac{\pi}{2}-{{ \theta}}\right)=sin({{ \theta}})
\\ \quad \\ \quad \\
tan\left(\frac{\pi}{2}-{{ \theta}}\right)=cot({{ \theta}})\qquad
cot\left(\frac{\pi}{2}-{{ \theta}}\right)=tan({{ \theta}})
\\ \quad \\ \quad \\
sec\left(\frac{\pi}{2}-{{ \theta}}\right)=csc({{ \theta}})\qquad
csc\left(\frac{\pi}{2}-{{ \theta}}\right)=sec({{ \theta}})\\\\
-------------------------------\\\\[/tex]
[tex]\bf \begin{array}{lcllclll}
sin(&90^o-\theta)&=&cos(&\theta)\\
&\uparrow &&&\uparrow \\
&3x+15&&&7x-2\\
&\downarrow \\
&90-(7x-2)
\end{array}
\\\\\\
90-(7x-2)=3x+15\implies 90-7x+2=3x+15
\\\\\\
92-15=10x\implies 77=10x\implies \cfrac{77}{10}=x[/tex]
