Some Applications Of Trigonometry

Question

In the given figure, find tan P - cot R.

Solution

Let
PQ = 12K
and
PR = 13K
Using Pythagoras theorem, we have
PR² = PQ² + QR²⇒(13K)² = (12K)² + QR²⇒169K² = 144K² + QR²⇒QR² = 169K² - 144K²⇒QR² = 25K²So, QR = 5K
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Now,
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Therefore,
$tanP minus cotR space equals space 5 over 12 minus 5 over 12 equals 0.$