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Bingel [31]
3 years ago
10

Verify the identity tan x + cot x =csc x× sec x

Advanced Placement (AP)
1 answer:
slava [35]3 years ago
7 0
Tan(x) + cot(x) can be expressed as the following:

\frac{sin(x)}{cos(x)} +  \frac{cos(x)}{sin(x)}

Find the common denominator:

\frac{sin^2(x)+cos^2(x)}{sin(x)cos(x)}

We can use a Pythagorean identity to replace sin^2(x) + cos^2(x) with 1.

So now we have \frac{1}{sin(x)cos(x)} or \frac{1}{sin(x)} * \frac{1}{cos(x)}

Which equals:

csc(x)sec(x)


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