[tex]3tan^{2} \theta +7sec\theta=3[/tex] First I converted the equation terms into sine and cosine. [tex]tan^{2}\theta = \frac{sin^{2}\theta}{cos^{2}\theta} [/tex] and [tex]sec\theta= \frac{1}{cos\theta} [/tex] Substitution: [tex] \frac{3sin^2\theta}{cos^2\theta} + \frac{7}{cos\theta} =3[/tex] Common Denominator Created: [tex] \frac{3sin^2\theta}{cos^2\theta} + \frac{7cos\theta}{cos^2\theta} =3[/tex] Multiply each term by the LCD: [tex]3sin^2\theta+7cos\theta=3cos^2\theta[/tex] Substitution: Recall ⇒[tex]sin^2\theta =1-cos^2\theta[/tex] [tex]3(1-cos^2\theta)+7cos\theta=3cos^2\theta[/tex] Distribute and collect all terms on one side: [tex]6cos^2\theta-7cos\theta-3=0[/tex] Factor and set each factor equal to 0: [tex](2cos\theta-3)(3cos\theta+1)=0[/tex] [tex]2cos\theta-3=0[/tex]⇒[tex]theta=cos^{-1} \frac{3}{2} [/tex] [tex]3cos\theta+1=0[/tex]⇒[tex]theta=cos^{-1} \frac{-1}{3} [/tex] The 2nd factor provides only possible answer 109.5 degrees
