Question

Tan^2x=3(secx-1), find x

Answer 1

Given that

tan²x = 3(secx - 1)

We know that

sec²x = tan²x + 1

→ tan²x = sec²x - 1

→ sec²x - 1 = 3(secx - 1)

→ (secx + 1)(secx - 1) = 3(secx - 1)

Cancel (secx - 1) from both sides

→ secx + 1 = 3

→ secx = 4

So x = sec-¹(4)

Answer 2

tan² x = 3(sec x - 1)

» sec² x - 1 = 3sec x - 3 {tan² x = sec² x - 1}

» sec² x - 3sec x + 2 = 0

» sec² x - 2sec x - sec x + 2 = 0

» sec x(sec x - 2) - 1(sec x - 2) = 0

» (sec x - 1)(sec x - 2) = 0

» sec x = 1 , 2

» x = 0°, 60°