Question

the distance between point A(cos x, sin x) and B(sin x, -cos x) is


A. root 3 units
B. root 2 units
C. 2 units
D. 1 unit​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

Hint: Start by considering the given two points as P(x1,y1) and Q(x2,y2)P(x1,y1) and Q(x2,y2) . Compare the coordinates for values and apply the formula for distance between two given points i.e. s=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√s=(x2−x1)2+(y2−y1)2

Simplify the values by using trigonometric identities ,to get the desired value.

Complete step by step answer:

Given

A(sin x , cos x) and B (cos x , -sin x)

We know that distance between two points P(x1,y1) and Q(x2,y2)P(x1,y1) and Q(x2,y2) is given by the formula s=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√s=(x2−x1)2+(y2−y1)2

We have [x1= sin x , y1=cos x][x2= cos x , y2= −sin x][x1= sin x , y1=cos x][x2= cos x , y2= −sin x]

Substituting these values in the formula we get

s=(cosx−sinx)2+((−sinx)−cosx)2−−−−−−−−−−−−−−−−−−−−−−−−−−−−√s=(cos⁡x−sin⁡x)2+((−sin⁡x)−cos⁡x)2

By using the formula

(a−b)2=a2+b2−2ab and (a+b)2=a2+b2+2ab=cos2x+sin2x−2sinxcosx+(−sinx)2+(cosx)2−2(−sinx)(cosx)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√=1−2sinxcosx+sin2x+cos2x+2sinxcosx−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√=1+1−−−−√S=2–√(a−b)2=a2+b2−2ab and (a+b)2=a2+b2+2ab=cos2x+sin2x−2sin⁡xcos⁡x+(−sin⁡x)2+(cos⁡x)2−2(−sin⁡x)(cos⁡x)=1−2sin⁡xcos⁡x+sin2x+cos2x+2sin⁡xcos⁡x=1+1S=2

So, the correct answer is “Option B”.