Question

if secx-tanx=m1 then tanx =? ​

Answer 1

Answer:

$tanx = \frac{1 - {(m1)}^{2} }{2m1}$

Step-by-step explanation:

GIVEN EQUATION HERE

=>secx-tanx=m1....... equation (1)

Apply this fomula

$1 + {tan}^{2} x = {sec}^{2} x \\ \\ \therefore \: {sec}^{2} x - {tan}^{2} x = 1 \\ \\ \therefore \: (secx - tanx)(secx + tanx) = 1 \\ \\ \therefore \: m1(secx + tanx) = 1 \\ \\ \therefore \: secx + tanx = \frac{1}{m1} ..........equation(2)$

Take Equation (2) - Equation (1)

$(secx + tanx) - (secx - tanx) = \frac{1}{m1} - m1 \\ \\ \therefore \: secx + tanx - secx + tanx = \frac{1 - {(m1)}^{2} }{m1} \\ \\ \therefore \: 2tanx = \frac{1 - {(m1)}^{2} }{m1} \\ \\ \therefore \: tanx = \frac{1 - {(m1)}^{2} }{2m1}$