Question
Very-Short and Short-Answer Qustions:
Write the value of $4\tan^2\theta-\frac{4}{\cos^2\theta}.$
Write the value of $4\tan^2\theta-\frac{4}{\cos^2\theta}.$
✓
Answer
$4\tan^2\theta-\frac{4}{\cos^2\theta}$
$=4\frac{\sin^2\theta}{\cos^2\theta}-\frac{4}{\cos^2\theta}$
$=\frac{4\sin^2\theta-4}{\cos^2\theta}$
$=\frac{4\big(\sin^2\theta-1\big)}{\cos^2\theta}$
$=\frac{4\times\big(-\cos^2\theta\big)}{\cos^2\theta}$
$=-4$
$=4\frac{\sin^2\theta}{\cos^2\theta}-\frac{4}{\cos^2\theta}$
$=\frac{4\sin^2\theta-4}{\cos^2\theta}$
$=\frac{4\big(\sin^2\theta-1\big)}{\cos^2\theta}$
$=\frac{4\times\big(-\cos^2\theta\big)}{\cos^2\theta}$
$=-4$
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