Question

Write the set of values of a for which the equation √3 sin x – cos x = a has no solution.

Answer 1

\(\frac{\sqrt3}2\) sin x - \(\frac{cosx}2\) = a

cos30°sin x – sin30°cos x = a 

sin (x - 30) = a 

As the range of sin function is from [-1,1] 

So the value of a can be R-[-1,1] 

i.e. a ∈ (-∞, -2) ∪ (2, ∞)