Can someone help with this? Please:Write 5 cos^2 (20 a) + 5 sin^2(20 a) as one trigonometric function.

Question

mathstudent55 · Answer

Do you know the identity:

$\sin^2 \theta + \cos^2 \theta = 1$

Factor out a 5. What do you get?

seattle12345 · Answer

$$5(\cos ^{2}\left( 20 a\right)+\sin ^{2}(20a))$$?

ranga · Answer

The one inside the parenthesis equals 1 because of the identity listed in the first reply.

seattle12345 · Answer

oh ok I see it.

mathstudent55 · Answer

Now apply the identity to what is inside the parentheses.

$5 \cos^2 20 a + 5 \sin^2 20 a$

$=5 \color{red}{( \cos^2 20 a +  \sin^2 20 a  )} $

$=5 \cdot \color{red}1 $

$ = 5$

seattle12345 · Answer

Thank you! I guess (20a) was confusing me a bit, but I see the identity

mathstudent55 · Answer

Right. The sine squared of anything plus the cosine squared of the same thing equals one, no matter what the thing is. In your case, the thing was 20a.