Question

Can someone PLEASE help me solve this equation ? due soon

Answer 1

`\sf{Given : 3tanx + 7 = (2)/((1 - sinx)(1 + sinx))}`

We know that : (a - b)(a + b) = a² - b²

`\implies \sf{3tanx + 7 = (2)/(1 - sin^2x)}`

We know that : 1 - sin²x = cos²x

`\implies \sf{3tanx + 7 = (2)/(cos^2x)}`

`\sf{\bigstar \ \ We \ know \ that : \boxed{\sf{(1)/(cos^2x) = sec^2x}}}`

`\implies \sf{3tanx + 7 = 2sec^2x}`

We know that : sec²x = 1 + tan²x

`\implies \sf{3tanx + 7 =2(1 + tan^2x)}`

`\implies \sf{2 + 2tan^2x - 3 tanx - 7 = 0}`

`\implies \sf{2tan^2x - 3 tanx - 5 = 0}`

`\implies \sf{2tan^2x - 5tanx + 2tanx - 5 = 0}`

`\implies \sf{2tanx(tanx + 1) - 5(tanx + 1) = 0}`

`\implies \sf{(tanx + 1)(2tanx - 5) = 0}`

`\implies \sf{tanx = -1 \ (or) \ tanx = (5)/(2) }`