Trig. Identities

**Googl** · February 9th 2011, 06:38 PM

Hi all,

I am revising maths trig I am trying to work out this.

Prove; $cos[theta] = 1-sin[alpha]tan([theta]/2)$

[theta] is alpha symbol.

I have tried but keep ending up with $sin^2([theta]/2) + sin^2([theta]/2)$

Thanks.

**topsquark** · February 9th 2011, 06:43 PM

Originally Posted by Googl

Hi all,

I am revising maths trig I am trying to work out this.

Prove; $cos[alpha] = 1-sinθtan([alpha]/2)$

[alpha] is alpha symbol.

I have tried but keep ending up with $sin^2([alpha]/2) + sin^2([alpha]/2)$

Thanks.

What is "sin(952)"?

and what does the tan function after it indicate?

-Dan

**Soroban** · February 9th 2011, 07:05 PM

Hello, Googl!

You should be familiar with these identities:

. . $\cos\theta \:=\:1-2\sin^2\frac{\theta}{2}$

. . $\sin\theta \:=\:2\sin\frac{\theta}{2}\cos\frac{\theta}{2}$

$\text{Prove: }\:\cos\theta \:=\: 1- \sin\theta\tan\frac{\theta}{2}$

$\text{The right side is: }\:1 - \left(2\sin\frac{\theta}{2}\cos\frac{\theta}{2}\ri ght)\left(\dfrac{\sin\frac{\theta}{2}}{\cos\frac{\ theta}{2}}\right)$

. . . . . . . . . . . $=\;1 - 2\sin^2\frac{\theta}{2}$

. . . . . . . . . . . $=\;\cos\theta$

**Googl** · February 9th 2011, 07:13 PM

Originally Posted by topsquark

What is "sin(952)"?

and what does the tan function after it indicate?

-Dan

Sorry that is supposed to be theta, I type it but does not come out right.

**Googl** · February 9th 2011, 07:19 PM

Originally Posted by Soroban

Hello, Googl!

You should be familiar with these identities:

. . $\cos\theta \:=\:1-2\sin^2\frac{\theta}{2}$

. . $\sin\theta \:=\:2\sin\frac{\theta}{2}\cos\frac{\theta}{2}$

$\text{The right side is: }\:1 - \left(2\sin\frac{\theta}{2}\cos\frac{\theta}{2}\ri ght)\left(\dfrac{\sin\frac{\theta}{2}}{\cos\frac{\ theta}{2}}\right)$

. . . . . . . . . . . $=\;1 - 2\sin^2\frac{\theta}{2}$

. . . . . . . . . . . $=\;\cos\theta$

Thanks.

I think I got to the identity 2sin(theta/2)cos(theta/2) but did not realise it was equal to $sin\theta$

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