Digital ACT Math Practice Question #2119
Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.
Plug in $\theta = 90^\circ$: $\sin 90^\circ = 1, \cos 90^\circ = 0$. Expression becomes $\frac{1^2}{1 - 0} = 1$. Check Choice A: $1 + \cos 90^\circ = 1 + 0 = 1$. Instant victory!
Substitute $\sin^2 \theta = 1 - \cos^2 \theta$. Factor the difference of squares in the numerator: $1 - \cos^2 \theta = (1 - \cos \theta)(1 + \cos \theta)$. Dividing by $(1 - \cos \theta)$ leaves $1 + \cos \theta$....
Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...
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