Use trigonometric identities to solve each equation within the given domain sec(x) cos(3x) = 0 from [- x /2 , x /2]

Either or .

Step-by-step explanation:

Angle sum identity for cosine:

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Double-angle identity for cosine and sine:

.

.

The secant of an angle is the inverse reciprocal of the cosine of that angle:

.

Apply these identities to rewrite the left-hand side of the equation.

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Solve the rewritten equation:

.

Either or .

The question required that . The sine function is one-to-one over this range. In other words, for each between and , there is exactly one between and such that .

If and , then .

Otherwise, if and , then ,

Verify that for either of the two values, such that the in the original equation takes a real value.

f

step-by-step explanation:

f

1. 2

2. 11

3. 5

4. 6

5. 7

6. 5

7. -1

8. 1

step-by-step explanation: