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Question 16
The value of the expression $$(\cos^6 \theta + \sin^6 \theta - 1)(\tan^2 \theta +Â \cot^2 \theta + 2)$$ is:
Solution
$$(\cos^6 \theta + \sin^6 \theta - 1)(\tan^2 \theta + \cot^2 \theta + 2)$$
Assume any value of $$\theta$$,
Let the $$\theta$$ be 45$$\degree$$,
= $$(\cos^6 45\degree + \sin^6 45\degree - 1)(\tan^2 45\degree + \cot^2 45\degree + 2)$$
=Â $$((\frac{1}{\sqrt{2}})^6 + (\frac{1}{\sqrt{2}})^6 - 1)(1 + 1 + 2)$$
= $$((\frac{1}{8}) + (\frac{1}{8}) - 1)(4)$$
= $$\frac{3}{4} \times 4$$
= -3
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