Question

In the given figure find tan P - cot R​

Answer 1

Step-by-step explanation:

tan P = P/B = 12/5

CotR = 5/12

tanP - cotR = 12/5 - 5/12

= 144 -25/60

= 119/60

I use here pythagoras theorem to find base of the right angle triangle

Whats the answer

Answer 2

❍ Given :-

In the ∆ PQR,

• PQ = 12 CM
• PR = 13 CM

To find :-

• Tan P - Cot R

Solution :-

First let's find out QR

By using Pythagoras Theorem,

we get,

$\sf{PQ^2+QR^2=PR^2}$

$\implies\sf{12^2+QR^2=13^2}$

$\implies\sf{144+QR^2=169}$

$\implies\sf{QR^2=169 - 144}$

$\implies\sf{QR = \sqrt{25} }$

$\implies\sf{QR = 5}$

Therefore the the three sides of the triangle are :-

• PQ = 12 CM
• QR = 5 CM
• PR = 13 CM

Now,

we know

$\bf {Tan \: p = \frac{P}{B}}$

And

$\bf \: Cot R = \frac{B}{P}$

Here,

$\bf\frac{P}{B} = \frac{QR}{RQ}$

And

$\bf\frac{B}{P} = \frac{QR}{RQ}$

Now,

Tan P - Cot R

$\implies\sf{\frac{P}{B} - \:\frac{B}{P}}$

$\implies\sf{\frac{QR}{RQ} - \:\frac{QR}{RQ}} </strong></p><p><strong>[tex]\implies\sf{\frac{QR}{RQ} - \:\frac{QR}{RQ}}$

$\implies \sf{ \frac{5}{12} - \frac{5}{12} } \\ \implies \sf { = 0}$

Therefore,

Your answer is 0