Question

1. The area of the triangle formed by the line x sin a + y cos a = sin2a with co-ordinate axes is
A) Sin2a B) cos2a C) 2sin2a D) 2cos2a

Answer 1

Answer:

Given x sin α + y cos α = sin 2α

Divide both sides by sin 2α

x/2 cos α + y/2 sin α = 1

This is of the form x/a +y/b = 1

We get a = 2 cos α, b = 2 sin α

Area of triangle = ½ |a×b|

= ½ (2 cos α× 2 sin α)

= 2 sin α cos α

= sin 2α

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given x sin α + y cos α = sin 2α

Divide both sides by sin 2α

x/2 cos α + y/2 sin α = 1

This is of the form x/a +y/b = 1

We get a = 2 cos α, b = 2 sin α

Area of triangle = ½ |a×b|

= ½ (2 cos α× 2 sin α)

= 2 sin α cos α

= sin 2α

part a