This is the problem from ISI MStat 2019 PSA Problem 15. First, try it yourself and then go through the sequential hints we provide.
How many solutions does the equation \( cos ^{2} x+3 \sin x \cos x+1=0\) have for \( x \in[0,2 \pi) \) ?
Trigonometry
Factorization
Answer: is 4
ISI MStat 2019 PSA Problem 15
Precollege Mathematics
Factorize and Solve.
\(\cos ^{2} x+3 \sin x \cos x + 1 = (2\cos x + \sin x)(\cos x +\sin x) = 0 \).
\( tanx = -2, tanx = -1 \).
Draw the graph.
So, if you see the figure you will find there are 4 such x for \( x \in[0,2 \pi) \).
