Question

Find the distance between the points (0, sec θ) and (–tan θ, 0).​

Answer 1

Answer:

answer detailed solution given

Answer 2

The distance between given points is √(sin² θ + 1)/cos θ.  

Given:

The points (0, sec θ) and (–tan θ, 0)  

To find:

Find the distance between the points  

Solution:

Formula used:

Distance between a point P (x, y) and origin O (x₁, y₁) is given by

Distance, OP = √(x₁ - x)² + (y₁ - y)²    

Here we have (0, sec θ) and (–tan θ, 0).​  

Take (x, y) = (0,  sec θ)  

and (x₁, y₁) = (–tan θ, 0)  

From the given formula,

Distance = √( –tan θ - 0)² + (0 - sec θ)²    

= √ tan² θ + sec² θ

= √(sin² θ/cos² θ+ 1/cos² θ )  

= √(sin² θ + 1/cos² θ )    

=√(sin² θ + 1)/cos θ  

Therefore,

The distance between given points is √(sin² θ + 1)/cos θ.    

Learn more about Distance between the points at  

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