3 years ago

Please answer both questions!! Will mark brainliest!!

Mathematics

1 answer:

musickatia [10]3 years ago

5 0

Answer:

#1- is C / #2- is b

Step-by-step explanation:

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3 years ago

Simplify the expression 1/√(1-cos^2 x) . Remember cos x= 1/csc x

Cerrena [4.2K]

First, we are going to use the Pythagorean identity: $sin^2(x)+cos^2(x)=1$ to rewrite our expression. Solving for $sin^2(x)$ in our Pythagorean identity we get that $sin^2(x)=1-cos^2(x)$ , so we can rewrite our expression as follows:
$\frac{1}{ \sqrt{1-cos^2(x)} } = \frac{1}{ \sqrt{sin^2(x)} } = \frac{1}{sin(x)}$

Next, we are going to use the trig identity: $csc(x)= \frac{1}{sin(x)}$ to completely simplify our expression:
$\frac{1}{sin(x)} =csc(x)$

We can conclude that $\frac{1}{ \sqrt{1-cos^2(x)} }=csc(x)$