Solving: $\frac{1}{\sec\left(a\right)^2}=\sin\left(a\right)^2\cos\left(a\right)^2+\cos\left(a\right)$
Exercise
$\frac{1}{\sec^2\left(x\right)}=\sin^2\left(a\right).\cos^2\left(a\right)+\cos\left(a\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation 1/(sec(a)^2)=sin(a)^2cos(a)^2+cos(a). Applying the trigonometric identity: \displaystyle\frac{1}{\sec^{n}(\theta)}=\cos^{n}(\theta). Group the terms of the equation by moving the terms that have the variable a to the left side, and those that do not have it to the right side. Factor the polynomial \cos\left(a\right)^2-\sin\left(a\right)^2\cos\left(a\right)^2-\cos\left(a\right) by it's greatest common factor (GCF): \cos\left(a\right). Break the equation in 2 factors and set each factor equal to zero, to obtain simpler equations.
Solve the trigonometric equation 1/(sec(a)^2)=sin(a)^2cos(a)^2+cos(a)
Final answer to the exercise
$a=\frac{1}{2}\pi+2\pi n,\:a=\frac{3}{2}\pi+2\pi n,\:a=0+2\pi n,\:a=2\pi+2\pi n\:,\:\:n\in\Z$