Question

8.13, find tan P – cot R


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Answer 1

Answer:

tanP - cotR = 0

Step-by-step explanation:

In the given triangle PQR, the given triangle is right angled at Q and the given measures are:

$\implies$PR = 13cm,

$\implies$PQ = 12cm

Since the given triangle is right angled triangle, to find the side QR, apply the Pythagorean theorem

According to Pythagorean theorem,

In a right- angled triangle, the squares of the hypotenuse side is equal to the sum of the squares of the other two sides.

$\implies$PR² = QR² + PQ²

Substitute the values of PR and PQ

$\implies$13² = QR² + 12²

$\implies$169 = QR²+144

$\implies$ QR²= 169−144

$\implies$QR² = 25

$\implies$ QR = √25 = 5

Therefore, the side QR = 5 cm $\red\bigstar$

Now, To find tan P – cot R:

According to the trigonometric ratio, the tangent function is equal to the ratio of the length of the opposite side to the adjacent sides, the value of tan (P) becomes

$\implies$ tan (P) = Opposite side /Hypotenuse

$\implies$ tan (P) = QR/PQ

$\implies$ tan (P) = 5/12

Since cot function is the reciprocal of the tan function, the ratio of cot function becomes,

$\implies$ Cot (R) = Adjacent side/Hypotenuse

$\implies$ Cot (R) = QR/PQ

$\implies$ Cot (R) = 5/12

Therefore,

$\implies$ tan (P) – cot (R) = 5/12 – 5/12 = 0

$\implies$ Therefore, tan(P) – cot(R) = 0. $\green\bigstar$