Question

if q cos A=p, find tan A- cot A in terms of p and q​

Answer 1

Answer:

Given:-

• qcos A = p

Find:-

• Find tan A- cot A

Solution:-

${ \to{ \sf{qcos \:A = p }}}$

${ \sf \to{cos \:A = \frac{p}{q} }}$

We know that cos θ = Adjacent /Hypotenuse

So, Adjacent = p

Hypotenuse = q

From Pythagoras theorm:-

${ \boxed{ \sf{ {hyp}^{2} = {opp}^{2} + {adj}^{2} }}}$

${ \to{ \sf{ {q}^{2} = {opp}^{2} + {p}^{2} }}}$

${ \to{ \sf{ {opp}^{2} = {q}^{2} - {p}^{2} }}}$

${ \sf{ \to{opp = \sqrt{ {q}^{2} - {p}^{2} } }}}$

So, the opposite side is √q²-p²

Tan A - Cot A:-

${ \to{ \sf{ \frac{opp}{adj} - \frac{adj}{opp} }}}$

${ \to{ \sf{ \frac{ \sqrt{ {q}^{2} - {p}^{2} } }{p} - \frac{p}{ \sqrt{ {q}^{2} - {p}^{2} } } }}}$

${ \to{ \sf{ \frac{ {q}^{2} - 2 {p}^{2} }{p \sqrt{ {q}^{2} - {p}^{2} } } }}}$

Therefore, Value of TanA - CotA is

q²-2p²/p√q²-p² .