Question 47

Find (1-$$sin^{2}\theta$$)($$tan^{2}\theta$$+1)-1

Solution

$$ sin^{2}\theta + cos^{2}\theta = 1 $$...............(1)
$$ 1 + tan^{2}\theta = sec^{2}\theta $$...............(2)

$$ sec^{2}\theta = \frac{1}{cos^{2}\theta} $$................(3)

$$ (1 - sin^{2}\theta)(tan^{2}\theta + 1) - 1 $$

solving

$$ (cos^{2}\theta)(sec^{2}\theta) - 1 $$

$$ cos^{2}\theta \times \frac{1}{cos^{2}\theta} - 1 = 1 - 1 = 0 $$

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