Math, asked by sharmaaisha26896, 9 months ago

find tan p- cot R if PQ=12, PRcm =13cm , and angle Q =90​

Answers

Answered by kshitiz8933
2

Step-by-step explanation:

given:

\text{In right angled $\triangle$PQR, PQ=12 cm and PR=13 cm}In right angled △PQR, PQ=12 cm and PR=13 cm

\textbf{To find:}To find:

tan\,P-cot\,RtanP−cotR

\textbf{Solution:}Solution:

\text{In right angled $\triangle$PQR, by Pythagoras theorem}In right angled △PQR, by Pythagoras theorem

\text{we get}we get

PR^2=PQ^2+QR^2PR

2

=PQ

2

+QR

2

13^2=12^2+QR^213

2

=12

2

+QR

2

169=QR^2+144169=QR

2

+144

\implies\,QR^2=25⟹QR

2

=25

\implies\,QR=5⟹QR=5

\text{Consider,}Consider,

tan\,P=\dfrac{QR}{PQ}tanP=

PQ

QR

\implies\bf\,tan\,P=\dfrac{5}{12}⟹tanP=

12

5

cot\,R=\dfrac{QR}{PQ}cotR=

PQ

QR

\implies\bf\,cot\,R=\dfrac{5}{12}⟹cotR=

12

5

\text{Now,}Now,

tan\,P-cot\,RtanP−cotR

=\dfrac{5}{12}-\dfrac{5}{12}=

12

5

12

5

=0=0

\therefore\textbf{The value of tan\,P-cot\,R is 0}∴The value of tanP-cotR is 0

Answered by amitsnh
2

Answer:

clearly, PQR is a right triangle with right angle at Q, hypotenuse as PR and one side as PQ

now

tanP - cotR

= QR/PQ - QR/PQ

= 0

Similar questions