Advanced trig identity question! (involving addition formula)

**LHS** · February 8th 2009, 04:45 AM

Not quite sure how to do this, I messed about with it for a bit and got
tan(theta)=0

The answers in the book are 0,90

Any help will be greatly appreciated!

**Moo** · February 8th 2009, 04:59 AM

Hello,

Originally Posted by LHS

Not quite sure how to do this, I messed about with it for a bit and got
tan(theta)=0

The answers in the book are 0,90

Any help will be greatly appreciated!

$\sin \theta+\cos \theta=1$

Like they said, multiply by $\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}$ :

$\frac{\sqrt{2}}{2} \sin \theta+\frac{\sqrt{2}}{2} \cos \theta=\frac{\sqrt{2}}{2}$

$\cos 45 \sin \theta+\sin 45 \cos \theta=\frac{\sqrt{2}}{2}$

$\sin(45+\theta)=\frac{\sqrt{2}}{2}$

**LHS** · February 8th 2009, 05:13 AM

Ah, I see, I managed to get that equation but for some reason I didn't realise you could solve it, I expanded it then divided through by cos and sin to get tan theta + 1 = 1, which got me 0, and 180!

Thanks!

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