Question 54
What is the value of
$$[\tan^2 (90 - \theta) - \sin^2 (90 - \theta)] \cosec^2 (90 - \theta) \cot^2 (90 - \theta)?$$
Solution
$$[(\sin^2 (90 - \theta)/\cos^2 (90 - \theta)) - \sin^2 (90 - \theta)] \cos^2 (90 - \theta) /(\sin^4 (90 - \theta))$$
=$$(\sin^2 (90 - \theta)(1-\cos^2 (90 - \theta)/(\cos^2 (90 - \theta))) \cos^2 (90 - \theta) /(\sin^4 (90 - \theta))$$
$$(1-\cos^2 (90 - \theta)$$=$$\sin^2 (90 - \theta)$$
=$$(\sin^4 (90 - \theta)(\cos^2 (90 - \theta)/( \cos^2 (90 - \theta) /(\sin^4 (90 - \theta)))$$
=1
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