# Some complex trigo equations

• Dec 11th 2010, 09:00 AM
liukawa
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 !
• Dec 11th 2010, 10:27 AM
worc3247
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.
• Dec 15th 2010, 05:24 AM
liukawa
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.
• Dec 15th 2010, 07:53 PM
SammyS
Quote:

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.

$\displaystyle 36=2\times 18$

• Dec 17th 2010, 12:39 PM
worc3247
$\displaystyle sin2A=sin3A$
$\displaystyle 2sinAcosA=sin(2A+A)$
$\displaystyle 2sinAcosA=sin2AcosA+sinAcos2A$
$\displaystyle 2sinAcosA=2sinA\cos^2 A+sinA\cos^2 A -\sin^3 A$
$\displaystyle sinA\neq0$
$\displaystyle \uptherefore 2cosA=3\cos^2 A - \sin^2 A$
You should now be able to solve this by using trig identities and then applying the quadratic formula.