Theta and alpha are each acute angles in standard position, sin theta = 3/5 and cos alpha = 12/13

a) Determine cos (alpha+theta)
b) Determine sin (theta + alpha)

Here's a list of all the basic trig identities you should know to do further trig identities:

and

and

and

Then, the square identities;







Addition and subtraction of angles;

and


and


and

Double Angles;





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OOOOO



Now use them to solve your questions. :)

For cos (alpha + theta)
would the answer be cos (12/13 + 4/5)?

No. Start by converting to

Now have a drawing, you know some of the Pythagorean triples I hope:

Then, substitute your values of sin theta, sin alpha, cos theta and cos alpha. Do the same procedure for the second one. :)

EDIT: The second triangle has a mistake.

OK this is what I got
sin alpha cos theta- sinalpha sintheta
= (12/13) (4/5) - (11/13) (3/5)
= 3/13

and for the second one

sin theta cos alpha - costheta sin alpha
= (3/5)(12/13) - (4 /5 ) (11/13)
= -11/65

Sorry, yesterday, it was very late and I was very tired. The second triangle has sides 12, 13, 5 instead of 12, 13, 11.

Ok you did the question well, except that you haven't notice my mistake over there. You understood the concept though, good! :) now, just re-work up the actual answers.