Question

if tan²x+ secx = 5 find cosx

Answer 1

Answer:

${sec}^{2} x - {tan}^{2} x = 1$

${tan}^{2} x = {sec}^{2} x - 1$

putting the value ...

${sec}^{2} x - 1 + secx = 5$

let secx=Y

${y}^{2} - 1 + y = 5$

${y}^{2} + y - 6 = 0$

${y}^{2} + 3y - 2y - 6 = 0$

y (y+3)-2 (y+3)=0

(y-2) (y+3)=0

y=2 , y= -3

y=secx=2

cosx= 1/secx=1/2