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

Answer: J.

Step-by-step explanation: -tanx i believe

Answer:

H: 2

Step-by-step explanation:

[tex]\frac{\sqrt{1-\cos ^2\left(x\right)}}{\sin \left(x\right)}+\frac{\sqrt{1-\sin ^2\left(x\right)}}{\cos \left(x\right)}[/tex]

LCM is [tex]\cos \left(x\right)\sin \left(x\right)[/tex]

Adjust fractions:

[tex]\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)}[/tex]

Combine:

[tex]\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)}[/tex]

--------------------------------------------------------

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

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

Therefore, [tex]\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)[/tex]

-----------------------------------------------------------------------------------------------

Similarly, [tex]1-\sin ^2\left(x\right)=\cos ^2\left(x\right)[/tex] so

[tex]\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)[/tex]

-------------------------------------------------------------------------------

We will finally end up with

[tex]\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)}[/tex]

Add:

[tex]\frac{2\sin \left(x\right)\cos \left(x\right)}{\sin \left(x\right)\cos \left(x\right)}[/tex]

Cancel out sin(x):

[tex]\frac{2\cos \left(x\right)}{\cos \left(x\right)}[/tex]

Cancel out cos(x):

[tex]2[/tex]

15.
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