+26404 tan^2(30)= 1/cos^2(30) - 1 explain why.
\(\begin{array}{rcl} \text{Use the Pythagorean identity } \sin^2{(\theta)} + \cos^2(\theta) =1 \\ \end{array}\)
\(\begin{array}{rcl} \sin^2{(30^{\circ})} + \cos^2(30^{\circ}) &=& 1 \qquad & | \qquad : \cos^2(30^{\circ})\\\\ \frac{\sin^2{(30^{\circ})} } {\cos^2(30^{\circ})} + \frac{ \cos^2(30^{\circ}) } {\cos^2(30^{\circ}) } &=& \frac{1} { \cos^2{(30^{\circ})} } \qquad & \frac{\sin^2{(30^{\circ})} } {\cos^2(30^{\circ})} = \tan^2{(30^{\circ})}\\\\ \tan^2{(30^{\circ})} + 1 &=& \frac{1} { \cos^2{(30^{\circ})} } \qquad & | \qquad -1\\\\ \mathbf{\tan^2{(30^{\circ})} }& \mathbf{=} & \mathbf{ \frac{1} { \cos^2{(30^{\circ})} } -1} \end{array}\)
+26404 tan^2(30)= 1/cos^2(30) - 1 explain why.
\(\begin{array}{rcl} \text{Use the Pythagorean identity } \sin^2{(\theta)} + \cos^2(\theta) =1 \\ \end{array}\)
\(\begin{array}{rcl} \sin^2{(30^{\circ})} + \cos^2(30^{\circ}) &=& 1 \qquad & | \qquad : \cos^2(30^{\circ})\\\\ \frac{\sin^2{(30^{\circ})} } {\cos^2(30^{\circ})} + \frac{ \cos^2(30^{\circ}) } {\cos^2(30^{\circ}) } &=& \frac{1} { \cos^2{(30^{\circ})} } \qquad & \frac{\sin^2{(30^{\circ})} } {\cos^2(30^{\circ})} = \tan^2{(30^{\circ})}\\\\ \tan^2{(30^{\circ})} + 1 &=& \frac{1} { \cos^2{(30^{\circ})} } \qquad & | \qquad -1\\\\ \mathbf{\tan^2{(30^{\circ})} }& \mathbf{=} & \mathbf{ \frac{1} { \cos^2{(30^{\circ})} } -1} \end{array}\)
