1.

If sec A + tan A = m, sec A.tan A = n and sec4 A – tan4 A = m2/2, then which of the following is TRUE?1. m2 – 3n = 02. m2 – n = 03. m2 = n4. m2 = 4n

Answer» Correct Answer - Option 4 : m2 = 4n

GIVEN:

sec A + tan A = m

sec A. tan A = n

sec4 A – tan4 A = m2/2

CONCEPT:

Trigonometry

CALCULATION:

sec A + tan A = m

⇒ (sec A + tan A)2 = m2

⇒ sec2 A + tan2 A + 2 sec A. tan A = m2

⇒ sec2 A + tan2 A + 2n = m2

⇒ sec2 A + tan2 A = m2 – 2n

Now,

sec4 A – tan4 A = m2/2

⇒ (sec2 A – tan2 A) (sec2 A + tan2 A) = m2/2   [sec2 A – tan2 A = 1]

⇒ 1 (sec2 A + tan2 A) = m2/2

⇒ m2 – 2n = m2/2

⇒ 2m2 – 4n = m2

⇒ m2 = 4n


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