# Thread: more identities.(in a hurry)

1. ## more identities.(in a hurry)

1)what is this equivalent to cos(180degrees + B) answer:-cosB

2)use an identity to find an exact value for sin 105degrees.

3)use an identity to find an exact value for 22.5degrees.

2. Originally Posted by Dave19

1)what is this equivalent to cos(180degrees + B) answer:-cosB
$\cos (180^{\circ} + B) = \cos 180^{\circ} \cos B - \sin 180^{\circ} \sin B$

But $\cos 180^{\circ} = -1$ and $\sin 180^{\circ} = 0$

$\cos (180^{\circ} + B) = \cos 180^{\circ} \cos B - \sin 180^{\circ} \sin B = (-1) \cos B = -\cos B
$

2)use an identity to find an exact value for sin 105degrees.

$\sin 105^{\circ} = \sin (90^{\circ} + 15^{\circ}) = \cos 15^{\circ}$

Use the double angle formula: $\cos 2x = 2cos^2x - 1$

put $x = 15^{\circ}$, since you already know $\cos 30^{\circ} = \frac{\sqrt{3}}2$.

3)use an identity to find an exact value for 22.5degrees.

DO you mean sin of 22.5 degrees or cosine of 22.5 degrees? Whoat does the phrase "exact value of 22.5 degrees mean"?

3. sorry its tan and can you try my other questions if you can find them.

4. its under urgent homework help i think

5. Originally Posted by Dave19
sorry its tan and can you try my other questions if you can find them.
$\tan 2x = \frac{2\tan x}{1 - \tan^2 x}$ and $\tan 45 = 1$

Now if x = 22.5, 2x = 45. So

$\tan 2x = \tan 45 = 1 = \frac{2\tan x}{1 - \tan^2 x}$

$1 = \frac{2\tan x}{1 - \tan^2 x}$

Now solve the above equation for tan x. It is a quadratic equation which you can easily solve.

6. i dont no how that will equal root2-1

7. Originally Posted by Isomorphism
$\tan 2x = \frac{2\tan x}{1 - \tan^2 x}$ and $\tan 45 = 1$

Now if x = 22.5, 2x = 45. So

$\tan 2x = \tan 45 = 1 = \frac{2\tan x}{1 - \tan^2 x}$

$1 = \frac{2\tan x}{1 - \tan^2 x}$

Now solve the above equation for tan x. It is a quadratic equation which you can easily solve.
$1 = \frac{2\tan x}{1 - \tan^2 x} \Rightarrow 1 - \tan^2 x = 2\tan x$

If it is hard for you to see, put $u =\tan x$,

$1 - \tan^2 x = 2\tan x \Rightarrow 1 - u^2 = 2u \Rightarrow u^2 +2u -1 = 0$

Now try solving it. Come on show us some effort... You want to learn, dont you?

Ask me if you dont know...