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Equation a sin 2x+ cos 2x = 2a-7 possesses a solution if... Find value(s) of a

Equation a sin 2x+ cos 2x = 2a-7 possesses a solution if... Find value(s) of a

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Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
cos2x can be written as 1 - 2 sin2 x so the equation becomes 
1 - 2 sin^2 x +a sin x + 7 - 2a = 0
 2 sin^2 x -a sin x - 8 + 2a =0
it is quadratic in sin x
so by using quadratic formula 
we get
sin x = a +-√a^2 -4 * 2(2a - 8)/4
on solving we get 
sin x = (a - 4 )/2
to find the possible values of a we will use the following inequation
as we know that value of sin x lies between -1 to 1 
-1
-2
2 
so for this range the solution of the trigonometric equation exists

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