Exercise
$3sin^2x-2cos^2x=1$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation 3sin(x)^2-2cos(x)^2=1. Applying the trigonometric identity: \sin\left(\theta \right)^2 = 1-\cos\left(\theta \right)^2. Multiply the single term 3 by each term of the polynomial \left(1-\cos\left(x\right)^2\right). Combining like terms -3\cos\left(x\right)^2 and -2\cos\left(x\right)^2. We need to isolate the dependent variable x, we can do that by simultaneously subtracting 3 from both sides of the equation.
Solve the trigonometric equation 3sin(x)^2-2cos(x)^2=1
Final answer to the exercise
$\sin\left(x\right)=\sqrt{\frac{3}{5}},\:\sin\left(x\right)=-\sqrt{\frac{3}{5}}\:,\:\:n\in\Z$