Question

if secA+TanA=4 then find the value of secA-tanA​

Answer 1

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Answer 2

The answer is 1/4

Given: sec A + tan A = 4  

To find: The value of sec A - tan A

Solution:

From trigonometric identities  sec²A - tan²A = 1

⇒ sec²A - tan²A = (sec A + tan A)(sec A - tan A)  [from (a² - b²) = (a+b)(a-b)]

⇒ (sec A + tan A)(sec A - tan A) = 1

⇒   (4)(sec A - tan A) = 1      [ from given data ]

⇒ (sec A - tan A)  = 1/4

Therefore, the value of sec A - tan A = 1/4

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