AP EAMCET201921 Apr 2019Evening ShiftMathematicsTrigonometric EquationsActual
Let x = a sin α θ cos α + 1 θ , y = a sin α + 1 θ cos α θ , θ ≠ n π 2 . If x 2 + y 2 m ( x y ) n is independent of θ , then the relation between α , m and n is
Options
- A2 m α = n ( 2 α + 1 )
- Bm + n = α
- C2 m α = 2 n α + m
- D2 m = ( 2 n + 1 ) α
Correct answer
A. 2 m α = n ( 2 α + 1 )
Step-by-step solution
It is given that x = a sin a θ cos a + 1 θ and y = a sin a + 1 θ cos a θ Now, x 2 + y 2 m ( x y ) n Substitute the values in the above expression. = a sin a θ cos a + 1 θ 2 + a sin a + 1 θ cos a θ 2 m a sin a θ cos α + 1 θ · a sin a + 1 θ cos a θ n Simplify the above equation. x = a 2 m sin 2 a θ cos 2 a θ m sin 2 θ + cos 2 θ m a 2 n sin 2 a + 1 θ cos 2 a + 1 θ n = a 2 m - 2 n sin 2 a θ cos 2 a θ m - n ( si