Question

IF SEC A IS EQUAL TO X+1/4X THEN PROVE SEC A + TAN A IS EQUAL TO 2X OR 1/2X

Answer 1

Hope that clears your doubt

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Answer 2

♧♧HERE IS YOUR ANSWER♧♧

Given that :

secA = x + 1/(4x)

Now, squaring both sides, we get :

sec²A = {x + 1/(4x)}²

=> 1 + tan²A = x² + 2.x.{1/(4x)} + 1/(16x²)

(since sec²A - tan²A = 1)

=> tan²A = x² + 1/2 + 1/(16x²) - 1

=> tan²A = x² - 1/2 + 1/(16x²)

=> tan²A = x² - 2.x.(1/4x) + 1/(16x²)

=> tan²A = {x - 1/(4x)}²

So,

either : tanA = x - 1/(4x)

or : tanA = - {x - 1/(4x)}

Now, when secA = x + 1/(4x) and tanA = x - 1/(4x),

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

Again, when secA = x + 1/(4x) and tanA = - {x - 1/(4x)},

secA + tanA = x + 1/(4x) - {x - 1/(4x)}

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

= 1/(2x)

Therefore, secA + tanA = 2x or 1/(2x).

♧♧HOPE THIS HELPS YOU♧♧