# Solve the equation cos θ + 4 cos 2θ = 3, giving all solutions in the interval 0◦ ≤ θ ≤ 180◦ how do we solve it ? .

Let

and you can work out the ones in the range.

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To solve the equation ( \cos \theta + 4 \cos 2\theta = 3 ) for ( 0^\circ \leq \theta \leq 180^\circ ):

- Apply the double-angle identity: ( \cos 2\theta = 2\cos^2 \theta - 1 ).
- Substitute ( \cos 2\theta ) with ( 2\cos^2 \theta - 1 ) in the equation.
- Rearrange the equation and combine like terms to form a quadratic equation in terms of ( \cos \theta ).
- Solve the quadratic equation for ( \cos \theta ) using standard methods like factoring, completing the square, or using the quadratic formula.
- After finding the values of ( \cos \theta ), determine corresponding values of ( \theta ) within the given interval ( 0^\circ \leq \theta \leq 180^\circ ).

Following these steps will yield the solutions for the given equation within the specified interval.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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