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fiasKO [112]
3 years ago
6

Simplify cosx ( tanx+cotx)

Mathematics
1 answer:
Soloha48 [4]3 years ago
4 0
The first step to solving this is to use tan(t) = \frac{sin(t)}{cos(t)} to transform this expression.
cos(x) × ( \frac{sin(x)}{cos(x)} + cot(x) )
Using cot(t) = \frac{cos(x)}{sin(x)},, transform the expression again.
cos(x) × ( \frac{sin(x)}{cos(x)} +  \frac{cos(x)}{sin(x)} )
Next you need to write all numerators above the least common denominator (cos(x)sin(x)).
cos(x) × \frac{sin(x)^{2} + cos(x)^{2}  }{cos(x)sin(x)}
Using sin(t)² + cos(t)² = 1,, simplify the expression. 
cos(x) × \frac{1}{cos(x)sin(x)}
Reduce the expression with cos(x).
\frac{1}{sin(x)}
Lastly,, use \frac{1}{sin(t)} = csc(t) to transform the expression and find your final answer.
csc(x)
This means that the final answer to this expression is csc(x).
Let me know if you have any further questions.
:)
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