Math question of trig identities

l don't understand this question

I assume it wants you to solve for B, what have you tried so far?

Also, is that -2sin(B) or -2sin(13) in the second bracket?

I assume it wants you to solve for B, what have you tried so far?

Also, is that -2sin(B) or -2sin(13) in the second bracket?

I think it's meant to be an identity (and it is!) if we assume all the trig arguments are B (or beta), Expand both brackets and collect terms - there are some sin^2 and cos^2 terms which should add up to 13 and a couple of 'cross terms' with opposite signs which should cancel out

OP: post your working if still stuck

Note that you made an error in your second line, in the very last bracket, it should be 3cosB

this has a knock on effect on the other lines.

Once you finish fixing all the expansions, what identities can you spot being usable here?

When you multiply the last 2 brackets next to each other, you get +9cosB and +4sinB. You should have +9cos^2B and +4sin^2B as you've done (3cosB)^2 and (4sinB)^2.

You seem to overall have an issue keeping track of the powers. Your line below that should read.

13cos^2(B) + 12cos(B)sin(B) + 13sin^2(B) - 12 cos(B)sin(B) = 13

This will further simplify to 13cos^2(B) + 13sin^2(B) = 13

I'm not sure what the question is asking from here on (i.e. did it just want this simplified form, or more? Because this equation is a multiplication of a very common identity, meaning it'll hold for all values of B).

When you multiply the last 2 brackets next to each other, you get +9cosB and +4sinB. You should have +9cos^2B and +4sin^2B as you've done (3cosB)^2 and (4sinB)^2.

You seem to overall have an issue keeping track of the powers. Your line below that should read.

13cos^2(B) + 12cos(B)sin(B) + 13sin^2(B) - 12 cos(B)sin(B) = 13

This will further simplify to 13cos^2(B) + 13sin^2(B) = 13

I'm not sure what the question is asking from here on (i.e. did it just want this simplified form, or more? Because this equation is a multiplication of a very common identity, meaning it'll hold for all values of B).

Thank u so much l know where l have done wrong now!