Question

question is in the attachment....

Answer 1

I have taken P in place of theta because of simplicity in writing

sec p = x – tan p

squaring both the sides

sec2 p = x2 – 2* x* tan p + tan2 p

sec2 p – tan2 p = x2 – 2* x* tan p

x2 – 2* x* tan p – 1 = 0

2* x* tan p = x2 – 1

tan p = (x2 – 1) / 2 x

Answer 2

Step-by-step explanation:

sec a+tan a=x- - -1

squaring both sides

(sec a+tan a)²=x²

sec²a+tan²a+2sec a.tan a=x²

1+tan²a+tan²a+2sec a.tan a=x² ( sec²a=1+tan²a)

1+2tan²a+2sec a.tan a=x²

2tan a(tan a+sec a)+1=x²

2tan a(x)+1=x² (from 1)

tan a=(x²-1)/2x