Question

$$( \sec ^ { 2 } A - 1 ) ( \operatorname { c o s e c } ^ { 2 } A - 1 ) = 1$$

Answer

$$o=(1/(sec(A)^2-1)+1)/(c*sec(A)^2)$$

Solution


Divide both sides by \(\sec^{2}A-1\).
\[co\sec^{2}A-1=\frac{1}{\sec^{2}A-1}\]
Add \(1\) to both sides.
\[co\sec^{2}A=\frac{1}{\sec^{2}A-1}+1\]
Divide both sides by \(c\).
\[o\sec^{2}A=\frac{\frac{1}{\sec^{2}A-1}+1}{c}\]
Divide both sides by \(\sec^{2}A\).
\[o=\frac{\frac{\frac{1}{\sec^{2}A-1}+1}{c}}{\sec^{2}A}\]
Simplify  \(\frac{\frac{\frac{1}{\sec^{2}A-1}+1}{c}}{\sec^{2}A}\)  to  \(\frac{\frac{1}{\sec^{2}A-1}+1}{c\sec^{2}A}\).
\[o=\frac{\frac{1}{\sec^{2}A-1}+1}{c\sec^{2}A}\]