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Core 3 trig, really stuck

Express tan(5/6pi-x) in terms of ttanx
Use sin(a-b)=cos(1/2pi-(a-b))=cos((1/2pi-a)+b)) to derive the formula for sin (a-b)
prove that cot(a+b)=cotacotb-1/cota+cotb
prove that tanA + tanB =sin(a+b)/cosAcosB
Original post by KSmith15
Express tan(5/6pi-x) in terms of ttanx
Use sin(a-b)=cos(1/2pi-(a-b))=cos((1/2pi-a)+b)) to derive the formula for sin (a-b)
prove that cot(a+b)=cotacotb-1/cota+cotb
prove that tanA + tanB =sin(a+b)/cosAcosB


Have you met the 'addition formulae' or 'compound angle identities'?

You have them for sin(A+/B) cos(A+/B) and tan(A+/B) :smile:
Reply 2
Yes I have but I don't understand as I keep getting the wrong answer
Reply 3
Original post by KSmith15
Express tan(5/6pi-x) in terms of ttanx
Use sin(a-b)=cos(1/2pi-(a-b))=cos((1/2pi-a)+b)) to derive the formula for sin (a-b)
prove that cot(a+b)=cotacotb-1/cota+cotb
prove that tanA + tanB =sin(a+b)/cosAcosB


start with the 4th one as it looks the most straightforward.

Write out the standard formula for sin(A + B). Divide this by cosAcosB and simplify. See what you get. Post back if still stuck :smile:
Original post by KSmith15
Yes I have but I don't understand as I keep getting the wrong answer


Post what you have done to 'be wrong'
It might help people iron out the errors/misconceptions :smile:
Reply 5
Okay for the first one I have got (-sqroot3/3 - tanx)/(1-sqroot3/3tanx)???
for the second one I have no clue what to do
For the third one I know you change it to 1/tan but I've never done that before with combined angles
i have worked out four and got the correct answer but I thought you had to go from left to right on identities??
Original post by KSmith15
Okay for the first one I have got (-sqroot3/3 - tanx)/(1-sqroot3/3tanx)???
for the second one I have no clue what to do
For the third one I know you change it to 1/tan but I've never done that before with combined angles
i have worked out four and got the correct answer but I thought you had to go from left to right on identities??


Well with 1/tan(a+b), just swap the numerator and denominator of the addition/subtraction formula. That's essentially doing 1/addition/subtractin formula
Original post by KSmith15
Okay for the first one I have got (-sqroot3/3 - tanx)/(1-sqroot3/3tanx)???
for the second one I have no clue what to do
For the third one I know you change it to 1/tan but I've never done that before with combined angles
i have worked out four and got the correct answer but I thought you had to go from left to right on identities??


With the later ones have you thought about writing tan(x) as sin(x)/cos(x) ?

Working with identities is about as 'free' as you will ever be allowed to be in A Level maths and you can decide to work (generally speaking from wherever you like). I would say its potentially less relevant in these questions though.

As for the sin and cosine one? are you chappy with cos(x) being sin(90-x) and vice versa?

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