Question

8. What is the distance between the
points P(m cos2a, m sin2a) and
Q(m cos2B, m sin2B)?​

Answer 1

Answer:

2m sin( a - b )

Explanation:

We Have :-

points:-

P(m cos2a, m sin2a)

Q(m cos2B, m sin2B)

To Find :-

Distance between the points

Formula Used :-

$distance \: formula \: = \sqrt{(a_{2} - a _{1} )^{2} +(b_{2} - b _{1} )^{2}}$

Solution :-

$\sqrt{(m \: cos2b - m \: cos2a )^{2} +(m \: sin2b - m \: sin2a )^{2}} \\ \\ \\ \sqrt{m^{2} \: ( - 2 \: cos2b \: cos2a - \: 2 \: sin2b \: sin2a + 2)} \\ \\ \\ m\sqrt{2(1 - ( cos2b \: cos2a + sin2b \: sin2a))} \\ \\ \\ m\sqrt{2(1 - cos(2a - 2b))} \\ \\ \\ m\sqrt{2(2 sin^{2} ( \dfrac{2a - 2b}{2} ))} \\ \\ \\ 2m \: sin(a - b)$

Answer 2

Answer:

2m sin( a - b )

Explanation:

We Have :-

points:-

P(m cos2a, m sin2a)

Q(m cos2B, m sin2B)

To Find :-

Distance between the points

Formula Used :-

distance \: formula \: = \sqrt{(a_{2} - a _{1} )^{2} +(b_{2} - b _{1} )^{2}}distanceformula=

(a

2

−a

1

)

2

+(b

2

−b

1

)

2

Solution :-

$$\begin{lgathered}\sqrt{(m \: cos2b - m \: cos2a )^{2} +(m \: sin2b - m \: sin2a )^{2}} \\ \\ \\ \sqrt{m^{2} \: ( - 2 \: cos2b \: cos2a - \: 2 \: sin2b \: sin2a + 2)} \\ \\ \\ m\sqrt{2(1 - ( cos2b \: cos2a + sin2b \: sin2a))} \\ \\ \\ m\sqrt{2(1 - cos(2a - 2b))} \\ \\ \\ m\sqrt{2(2 sin^{2} ( \dfrac{2a - 2b}{2} ))} \\ \\ \\ 2m \: sin(a - b)\end{lgathered}$$