Question

If secA+tanA=x, then find tan

Answer 1

Answer:

Given secA + tanA = x

→ (1) Recall that sec2A − tan2A = 1

⇒ (secA + tanA)(secA − tanA) = 1

⇒x (secA − tanA) = 1

⇒(secA − tanA) = 1/x

→ (2) Subtract (2) from (1), we get (secA + tanA) − (secA − tanA) = x − (1/x)

⇒ secA + tanA − secA + tanA = (x2 − 1)/x

⇒ 2tanA = (x2 − 1)/x

∴ tanA = (x2 − 1)/ 2x

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Answer 2

The answer is (x^2-1)/2x