stryns dif \( 7.1 .1 \tan 40^{\circ} \) \( 7.1 .2 \cos ^{2} 130^{\circ} \) \( 7.1 .3 \cos 225 \) 7.2 Without using a calcelator, simplify the following expression: \[ \sin 237^{\circ} \cos 147^{\circ}-\frac{\cos 213^{\circ} \cdot \cos 393^{\circ}}{\tan 237^{\circ}} \] (7) 115 QUESTION 8 8.1 Prove the identity: \[ \tan x=\frac{1-\cos 2 x-\sin x}{\sin 2 x-\cos x} \] (5) 82 For which values of \( x \) in the interval \( x \in\left[0^{\circ}, 270^{\circ}\right] \) is the identity not defined? \( (7) \) \( \cdots \)

A fun fact about the tangent function is its connection to the unit circle! The angle where the tangent function equals the slope of the radius that intercepts the circle represents how the function can be visualized geometrically. So, when you're working with angles like \(40^{\circ}\) or \(130^{\circ}\), think of it as tracing the circle and observing their slopes! When it comes to simplifying trigonometric expressions, keep an eye out for common angles and identities. One common pitfall is forgetting that \( \tan \theta = \frac{\sin \theta}{\cos \theta} \), so be sure to use this to your advantage when tackling those identities and simplifying expressions. Also, don't forget to convert angles exceeding \(360^{\circ}\) into the equivalent angle in the standard position to simplify your calculations!