# Thread: Some complex trigo equations

1. ## 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

Thanks !

2. 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.

3. 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.

4. Originally Posted by liukawa

But i kinda don't understand qn 3

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

$36=2\times 18$

5. $sin2A=sin3A$
$2sinAcosA=sin(2A+A)$
$2sinAcosA=sin2AcosA+sinAcos2A$
$2sinAcosA=2sinA\cos^2 A+sinA\cos^2 A -\sin^3 A$
$sinA\neq0$
$\uptherefore 2cosA=3\cos^2 A - \sin^2 A$
You should now be able to solve this by using trig identities and then applying the quadratic formula.