Write Then simplify the expression so no quotients appear

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.

x> 6

step-by-step explanation:

8x+8> 7x+14

8x-7x> 14-8

x> 6

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)