Match the right side of the equation to the left side
cot x sec^4 x=cot x+ 2 tan x+tan^3 x

Step-by-step explanation:

cot x + 2 tan x + tan³ x

Write in terms of sine and cosine:

(cos x / sin x) + 2 (sin x / cos x) + (sin³ x / cos³ x)

Find the common denominator:

(cos⁴ x / (sin x cos³ x) + 2 (sin² x cos² x / (sin x cos³ x)) + (sin⁴ x / (sin x cos³ x))

Add:

(cos⁴ x + 2 sin² x cos² x + sin⁴ x) / (sin x cos³ x)

Factor:

(sin² x + cos² x)² / (sin x cos³ x)

Pythagorean identity:

1 / (sin x cos³ x)

Multiply top and bottom by cos x:

cos x / (sin x cos⁴ x)

Simplify:

cot x sec⁴ x

Final cost of the subscription for 7 days will be $115.748

Step-by-step explanation:

30 days subscription = $499 + 8% tax

So subscription for 30 days = 499 +

= $499 + $39.92

= $538.92

Since we have to calculate the cost of the subscription for the 7 days on the prorated basis.

Therefore, total subscription for 7 days = Subscription for one day × number of days

=

= 17.964 × 7

= $125.748

Since we have a coupon for $10 off so the final cost will be = $125.75 - $10

= $115.748

Final cost of the subscription for 7 days will be $115.748