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# ISI MStat 2019 PSA Problem 15 | Trigonometry Problem

This is the problem from ISI MStat 2019 PSA Problem 15. First, try it yourself and then go through the sequential hints we provide.

## Trigonometry - ISI MStat Year 2019 PSA Question 15

How many solutions does the equation $cos ^{2} x+3 \sin x \cos x+1=0$ have for $x \in[0,2 \pi)$ ?

• 1
• 3
• 4
• 2

### Key Concepts

Trigonometry

Factorization

ISI MStat 2019 PSA Problem 15

Precollege Mathematics

## Try with Hints

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 $x \in[0,2 \pi)$.