Question

Evaluate the expression:
sin 30 degrees cos 60 degrees + sin 60 degrees cos 30 degrees

Answer 1

Recall the double angle formula here, thus expression = sin (30 + 60) = sin90 = 1

Answer 2

okay

Answer 3

what about (cos 30 degrees)^2 - (sin30degrees)^2

Answer 4

Likewise double angle, cos(30+30)= cos(60) = 1/2

Answer 5

hmm my teacher never said anything about this double angle formula!!! ugh summer school. Thanks

Answer 6

this isnt double angle actually..

Answer 7

are you familiar with this @Lanik
\[\large \sin (\alpha + \beta) = \sin \alpha \cos \beta + \sin \beta \cos \alpha\]

Answer 8

Oops typo my bad. The first case should have been compound angle formula.

Answer 9

yep better

Answer 10

i didnt notice the question changed lol

Answer 11

@Lanik if you're interested to "derive" the double angle formula..

\[\cos (\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta\]
\[\text{If} \quad \alpha = \beta\]
\[\cos (\alpha + \alpha) = \cos \alpha \cos \alpha - \sin \alpha \sin alpha\]
\[\cos(2\alpha) = \cos^2 \alpha - \sin^2 \alpha\]