Question

Write n^{2} x)" alt="cot^{2} x (1+tan^{2} x)" align="absmiddle" class="latex-formula"> Then simplify the expression so no quotients appear

Answer 1

Step-by-step explanation:

From Trig

1 + tan²x = Sec²x

Also

Sec²x = 1/cos²x

Now

Cot²x = 1/tan²x = cos²x/sin²x

Putting all together

Cot²x(1+tan²x)

= Cot²x(sec²x)

= cos²x/sin²x(1/cos²x)

cos²x on the numerator and that one the denominator cancels out

we have

= 1/sin²x

From Trig

1/sin²x = cosec²x

So Our Answer = cosec²x.