Question

Find the acute and obtuse angle between the following pairs of straight lines:
x sec(theta)+y cosec(theta)=a, x cos(theta)+y sin(theta)=a cos2 theta

Answer 1

Answer:2

π

​  

 

y  

2

sin  

2

θ−xysin  

2

θ+x  

2

(cos  

2

θ−1)=0  

y  

2

sin  

2

θ−xysin  

2

θ−x  

2

sin  

2

θ=0

we know that for ax  

2

+by  

2

+2hxy=0 if a+b=0 then the pair of lines are perpendicular

Here a=sin  

2

θ,b=−sin  

2

θ⇒a+b=0

Hence, the lines are perpendicular

Step-by-step explanation: