Trigonometric EquationHard
Question
Consider three points P = (-sin(β - α), - cosβ), Q = (cos(β - α), sinβ) and R = (cos(β - α + θ), sin(β - θ)), where 0 < α, β, θ < 
. Then
. Then Options
A.P lies on the line segment RQ
B.Q lies on the line segment PR
C.R lies on the line segment QP
D.P, Q, R are non-collinear
Solution
P ≡ ( - sin(β - α), - cos β) ≡ (x1, y1)
Q ≡ (cos(β - α), sin β) ≡ (x2, 2)
and R ≡ (x2cos θ + x1 sin θ, y2 cos θ + y1 sinθ
We see that T ≡
and P, Q, T are collinear
⇒ P, Q, R are non-collinear.
Q ≡ (cos(β - α), sin β) ≡ (x2, 2)
and R ≡ (x2cos θ + x1 sin θ, y2 cos θ + y1 sinθ
We see that T ≡
and P, Q, T are collinear
⇒ P, Q, R are non-collinear.
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