Find the exact value of $\sin^2\left(20^\circ\right)+\cos^2\left(20^\circ\right)$sin2(20°)+cos2(20°).
Given that $\cos x=\frac{12}{13}$cosx=1213 where $x$x is in the first quadrant, answer the following questions.
Given that $\sin\theta=\frac{\sqrt{3}}{2}$sinθ=√32 for $90^\circ<\theta<180^\circ$90°<θ<180°, find the value of $\cos\theta$cosθ using the Pythagorean identity.
Simplify $\tan\theta\cos\theta$tanθcosθ.