Thread: Some complex trigo equations

Hi Guys.

am stuck with a few trigo questions here ...

1) Find value of sin10 + sin50 - sin70 without using calculator

2) Prove that sin(A+2B) + sin(A-2B) = 4sinAsinBcosB

3) If A =36 , show that sin3A = Sin 2A and find cos 36

Appreciate your help guys !

Thanks !

1) Note that 10=30-20, 50=30+20 and 70=90-20. Then think sin(A+B)=sinAcosB+sinBcosA.
2) Again this is just trig formula sin(A+B)=sinAcosB+sinBcosA and the one for cos as well.
3) 3A=108 2A=72. Note that 90+18=108 and 90-18=72 and then look at a graph of y=sin(x).
Let me know how you get on.

Hi Thanks for your help.

But i kinda dont understand qn 3

how does looking at the sin curve help me to deduce the value of cos36.

Originally Posted by liukawa

Hi Thanks for your help.

But i kinda don't understand qn 3

how does looking at the sin curve help me to deduce the value of cos36.

You should now be able to solve this by using trig identities and then applying the quadratic formula.