if tana+secan a=x then tana=
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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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