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Question 39
What is the value of $$\cosec(65^\circ + \theta) - \sec(25^\circ - \theta) + \tan^2 20^\circ - \cosec^2 70^\circ $$ ?
Solution
$$\cosec(65^\circ + \theta) - \sec(25^\circ - \theta) + \tan^2 20^\circ - \cosec^2 70^\circ $$
=$$\cosec(65^\circ + \theta) - \sec(90 -Â (65^\circ + \theta)) + \tan^2 20^\circ - \cosec^2 (90 - 20)$$
=$$\cosec(65^\circ + \theta) - \cosec(65^\circ + \theta) + \tan^2 20^\circ - \sec^2 20^\circ$$
=$$ \tan^2 20^\circ - \sec^2 20^\circ$$
=$$ -(\sec^2 20^\circ -\tan^2 20^\circ )$$ = -1
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