![\sf{Given : 3tanx + 7 = \dfrac{2}{(1 - sinx)(1 + sinx)}}](https://tex.z-dn.net/?f=%5Csf%7BGiven%20%3A%203tanx%20%2B%207%20%3D%20%5Cdfrac%7B2%7D%7B%281%20-%20sinx%29%281%20%2B%20sinx%29%7D%7D)
We know that : (a - b)(a + b) = a² - b²
![\implies \sf{3tanx + 7 = \dfrac{2}{1 - sin^2x}}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B3tanx%20%2B%207%20%3D%20%5Cdfrac%7B2%7D%7B1%20-%20sin%5E2x%7D%7D)
We know that : 1 - sin²x = cos²x
![\implies \sf{3tanx + 7 = \dfrac{2}{cos^2x}}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B3tanx%20%2B%207%20%3D%20%5Cdfrac%7B2%7D%7Bcos%5E2x%7D%7D)
![\sf{\bigstar \ \ We \ know \ that : \boxed{\sf{\dfrac{1}{cos^2x} = sec^2x}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbigstar%20%5C%20%5C%20We%20%5C%20know%20%5C%20that%20%3A%20%5Cboxed%7B%5Csf%7B%5Cdfrac%7B1%7D%7Bcos%5E2x%7D%20%3D%20sec%5E2x%7D%7D%7D)
![\implies \sf{3tanx + 7 = 2sec^2x}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B3tanx%20%2B%207%20%3D%202sec%5E2x%7D)
We know that : sec²x = 1 + tan²x
![\implies \sf{3tanx + 7 =2(1 + tan^2x)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B3tanx%20%2B%207%20%3D2%281%20%2B%20tan%5E2x%29%7D)
![\implies \sf{2 + 2tan^2x - 3 tanx - 7 = 0}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B2%20%2B%202tan%5E2x%20-%203%20tanx%20-%207%20%3D%200%7D)
![\implies \sf{2tan^2x - 3 tanx - 5 = 0}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B2tan%5E2x%20-%203%20tanx%20-%205%20%3D%200%7D)
![\implies \sf{2tan^2x - 5tanx + 2tanx - 5 = 0}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B2tan%5E2x%20-%20%205tanx%20%2B%202tanx%20-%205%20%3D%200%7D)
![\implies \sf{2tanx(tanx + 1) - 5(tanx + 1) = 0}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B2tanx%28tanx%20%2B%201%29%20-%205%28tanx%20%2B%201%29%20%3D%200%7D)
![\implies \sf{(tanx + 1)(2tanx - 5) = 0}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7B%28tanx%20%2B%201%29%282tanx%20-%205%29%20%3D%200%7D)
![\implies \sf{tanx = -1 \ (or) \ tanx = \dfrac{5}{2} }](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%7Btanx%20%3D%20-1%20%5C%20%28or%29%20%5C%20tanx%20%3D%20%5Cdfrac%7B5%7D%7B2%7D%20%7D)
Please take a photo of this problem... it looks very hard when it is written in the way you did.
<h3>
If I am reading this correctly the answer should be 1,977,326,743x^3</h3>
Answer:
x = 21/10
Step-by-step explanation:
3/10 = x/7
Cross multiply.
10x = 21
x = 21/10
Answer:
Step-by-step explanation:
x + 40 = 10
x = -30
She paid $30 on her credit card