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kaheart [24]
3 years ago
14

Write the expression in terms of sine and cosine and simplify so that no quotients appear in the final expression. Show work.

Mathematics
1 answer:
AlexFokin [52]3 years ago
7 0
<h3>Answer:</h3>

sec²(x)

<h3>Explanation:</h3>

As required:

... = (sin²(x)/cos²(x))(1 +(cos²(x)/sin²(x))

... = (sin²(x)·(sin²(x)+cos²(x)) / (cos²(x)·sin²(x))

... = 1/cos²(x) = sec²(x)

_____

Alternatively, multiply out the given expression, then use trig identities.

... = tan²(x) + (tan(x)·cot(x))² = tan²(x) +1 = sec²(x)

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