Answer:
tan²x + 1 = sec²x is identity
Step-by-step explanation:
* Lets explain how to find this identity
∵ sin²x + cos²x = 1 ⇒ identity
- Divide both sides by cos²x
∵ sin x ÷ cos x = tan x
∴ sin²x ÷ cos²x = tan²x
- Lets find the second term
∵ cos²x ÷ cos²x = 1
- Remember that the inverse of cos x is sec x
∵ sec x = 1/cos x
∴ sec²x = 1/cos²x
- Lets write the equation
∴ tan²x + 1 = 1/cos²x
∵ 1/cos²x = sec²x
∴ than²x + 1 = sec²x
- So we use the first identity sin²x + cos²x = 1 to prove that
tan²x + 1 = sec²x
∴ tan²x + 1 = sec²x is identity
<em><u>Problem One</u></em>
Remark
You don't pay a sales tax until cash is exchanged for goods or services.
So what is 70% off
Solution
Sale price = given price * (100% - 70%)
Sale Price = 72 * 30%
Sale Price = 72 * 30/100
Sale Price = 72 * 0.3
Sale Price = 21.6 dollars.
The sales tax is 5% of this amount
21.6 * 5/100 = 1.08
The total cost is = 21.6 + 1.08 = 22.68
Problem Two
If they marked up 100%, effectively they doubled the price.
New Price = old price + 100% of old price.
New Price = 48.50 + 48.50 = 97 dollars.
The sales tax is 6% * 97 = 6/100 * 97 = 5.82
Total Cost = Cost of item + Tax
Total Cost =97 + 5.82
Total Cost = 102.82 Answer <<<<
