Question

if sec a = X + 1 upon 4 x, then prove that sec a + tan a = 2x or 1 upon 2 x​

Answer 1

Answer:

secA=x+1/4x

sec²A=(x+1/4x)²

sec²A=x²+1/2+1/16x²

1+tan²A=x²+1/2+1/16x²

tan²A=x²+1/2-1+1/16x²

tan²A=x²-1/2+1/16x²

tan²A=(x-1/4x)²

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

secA+tanA=x+1/4x+x-1/4x=2x

secA+tanA=x+1/4x-x+1/4x=2/4x=1/2x

Answer 2

Answer:on squaring both sides

Sec^2a = (x + 1/4x)^2

Sec^2a = 1+ tan^2a

So

Tan^2a = x^2 + 1/16x^2 +1/2 - 1

Tan^2a = x^2 + 1/16x^2 - 1/2

Tan^2a = (x - 1/4x)^2

So, Tan a = +/- (x - 1/4x)

Sec a + Tan a = x + 1/4x + x -1/4x

Sec a + Tan a = 2x

OR

Sec a + Tan a = x + 1/4x - (x - 1/4x)

Sec a + Tan a = 1/2x

Step-by-step explanation: