Question

Could someone help me with this trig question?

Answer 1

k= 5.

Explanation:

1. Write the expression.

`ksin^(2) (x)+kcos^(2) (x)=5`

2. Factorize k.

`k(sin^(2) (x)+cos^(2) (x))=5`

3. Simplify using pythagorean identities.

Check attached image 1.

`k(1)=5\\ \\k=5`

4. Verify.

Let's graph the function to see if it's true that it equals 5 for any value of x and k=5.

Check attached image 2.

As we can see in the graph, for any value of x the function returns 5. Hence, the answer is correct.