1. ## Verify Identity

I having trouble on verify identitys can somone please explain how to do these?

*0=theta*

a. Tan0sin0+cos0=sec0

b. sec^(4)x-tan^(4)x=sec^(2)x+tan^(2)x

2. A)

$\displaystyle tan(\theta)\cdot sin(\theta) + cos(\theta)=\frac{1}{cos(\theta)}$

$\displaystyle \frac{sin^{2}(\theta)}{cos(\theta)}+cos(\theta)=\f rac{1}{cos(\theta)}$

$\displaystyle sin^{2}(\theta) + cos^{2}(\theta) = \frac{cos(\theta)}{cos(\theta)} = \mbox{ Trig. identity } = 1$

3. Hello, goldenroll!

$\displaystyle a)\;\;\tan\theta\sin\theta +\cos\theta \:=\:\sec\theta$
$\displaystyle \tan\theta\sin\theta + \cos\theta \:=\:\frac{\sin\theta}{\cos\theta}\cdot\sin\theta + \cos\theta \;=\;\frac{\overbrace{\sin^2\!\theta + \cos^2\!\theta}^{\text{This is 1}}}{\cos\theta} \;=\;\frac{1}{\cos x} \;=\;\sec x$

$\displaystyle b)\;\;\sec^4\!x-\tan^4\!x \;=\;\sec^2\!x+\tan^2\!x$
$\displaystyle \sec^4\!x - \tan^4\!x \;=\;\overbrace{(\sec^2\!x-\tan^2\!x)}^{\text{This is 1}}(\sec^2\!x + \tan^2\!x) \;=\; \sec^2\!x + \tan^2\!x$