Question

secA=x+1/4x . prove that secA+tanA=2x or 1/2x solve in detail​

Answer 1

Step-by-step explanation:

SecA = x +1/4x

∴, Sec²A = (x+1/4x)²

= x² + 2.x.1/4x + 1/16x²

= x² + 1/2 + 1/16x²

Now,

Sec²A - Tan²A = 1

⇒ Tan²A = Sec²A - 1

⇒ Tan²A = x² + 1/2 + 1/16x² - 1

⇒ Tan²A = x² + 1/16x² - 1/2

⇒ Tan²A = x² - 2.x.1/4x + 1/16x²

⇒ Tan²A = (x-1/4x)²

⇒ TanA = ± (x-1/4x)

∴

CASE 1: TanA = x - 1/4x

SecA + TanA

= x + 1/4x + x -1/4x

= 2x

CASE 2: TanA = -(x - 1/4x)

SecA + TanA

= x + 1/4x - (x - 1/4x)

=x + 1/4x - x + 1/4x

= 1/4x + 1/4x

= 2/4x

= 1/2x (Proved)