Question

In diagram , Find tan P - Cot R

Answer 1

Given:-    

• PQ = 12 cm
• PR = 13 cm

To find:-    

• tan P - cot R

Solution:-  

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad\qquad\qquad}$

Finding side QR,

~Applying Pythagoras theorem

$\qquad\sf{:\implies\:(\:Hypotenuse\:)^{2}\:=\:(\:Height\:)^{2}\:+\:(\:Base\:)^{2}}$

$\qquad\sf{:\implies\:(\:PR\:)^{2}\:=\:(\:PQ\:)^{2}\:+\:(\:QR\:)^{2}}$

$\qquad\sf{:\implies\:(\:13\:)^{2}\:=\:(\:12\:)^{2}\:+\:(\:QR\:)^{2}}$

$\qquad\sf{:\implies\:169\:=\:144\:+\:(\:QR\:)^{2}}$

$\qquad\sf{:\implies\:(\:QR\:)^{2}\:=\:169\:-\:144}$

$\qquad\sf{:\implies\:(\:QR\:)^{2}\:=\:25}$

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

$\qquad\sf{:\implies\:QR\:=\:5\:cm}$

Therefore side QR is 5 cm.

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad\qquad\qquad}$

~Now tan P

$\qquad\sf{:\implies\:tan\:P\:=\:\dfrac{QR}{PQ}}$

$\qquad\sf{:\implies\:tan\:P\:=\:\dfrac{5}{12}}$

Therefore tan P is 5/12

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad\qquad\qquad}$

~Now cot R

$\qquad\sf{:\implies\:cot\:R\:=\:\dfrac{QR}{PQ}}$

$\qquad\sf{:\implies\:cot\:R\:=\:\dfrac{5}{12}}$

Therefore cot R is 5/12

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad\qquad\qquad}$

~finding tan P - Cot R

$\qquad\sf{:\implies\:tan\:P\:-\:cot\:R}$

$\qquad\sf{:\implies\:\dfrac{5}{12}\:-\dfrac{5}{12}}$

$\qquad\sf{:\implies\:0}$

Answer 2

Answer:

• Correct answer is 0

Step-by-step explanation: