Question

HELPPPPP!!!! tHIS IS REALLY HARD!!!!!

Answer 1

Answer: J.

Step-by-step explanation: -tanx i believe

Answer 2

Answer:

H: 2

Step-by-step explanation:

$\frac{\sqrt{1-\cos ^2\left(x\right)}}{\sin \left(x\right)}+\frac{\sqrt{1-\sin ^2\left(x\right)}}{\cos \left(x\right)}$

LCM is $\cos \left(x\right)\sin \left(x\right)$

Adjust fractions:

$\frac{\sqrt{1-\cos ^2\left(x\right)}\cos \left(x\right)}{\sin \left(x\right)\cos \left(x\right)}+\frac{\sqrt{1-\sin ^2\left(x\right)}\sin \left(x\right)}{\cos \left(x\right)\sin \left(x\right)}$

Combine:

$\frac{\sqrt{1-\cos ^2\left(x\right)}\cos \left(x\right)+\sqrt{1-\sin ^2\left(x\right)}\sin \left(x\right)}{\sin \left(x\right)\cos \left(x\right)}$

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We will take a look at $\sqrt{1-\cos ^2\left(x\right)}\cos \left(x\right)$.

Using the identity that $\cos ^2\left(x\right)+\sin ^2\left(x\right)=1$, we know that $1-\cos ^2\left(x\right)=\sin ^2\left(x\right)$.

Therefore, $\sqrt{1-\cos ^2\left(x\right)}\cos \left(x\right)=\sqrt{\sin ^2\left(x\right)}\cos \left(x\right)=\sin \left(x\right)\cos \left(x\right)$

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Similarly, $1-\sin ^2\left(x\right)=\cos ^2\left(x\right)$ so

$\sqrt{1-\sin ^2\left(x\right)}\sin \left(x\right)=\sqrt{\cos ^2\left(x\right)}\sin \left(x\right)=\cos \left(x\right)\sin \left(x\right)$

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We will finally end up with

$\frac{\sin \left(x\right)\cos \left(x\right)+\cos \left(x\right)\sin \left(x\right)}{\sin \left(x\right)\cos \left(x\right)}$

Add:

$\frac{2\sin \left(x\right)\cos \left(x\right)}{\sin \left(x\right)\cos \left(x\right)}$

Cancel out sin(x):

$\frac{2\cos \left(x\right)}{\cos \left(x\right)}$

Cancel out cos(x):

$2$