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.
Create a free account to view solution
View Solution FreeMore Trigonometric Equation Questions
If in a triangle PQR, sin P, sin Q, sin R are in AP, then...The general solution of tan 3x = 1 is -...If tan A + tan B + tan C = tan A. tan B. tan C then -...The resultant of forces and is . If is doubled then is doubled. If the direction of is reversed, then is again doubled. ...If one of the lines of my2 + (1 - m2)xy - mx2 = 0 is a bisector of the angle between the lines xy = 0, then m is...