Question
If secx – tanx = 1/√3, then the value of secx × tanx
is:Solution
Since, secx – tanx = 1/√3………………(1)
And, sec 2 x – tan 2 x = 1
(secx + tanx)(secx – tanx) = 1
So, secx + tanx = √3………………….(2)
From equation (1) and (2), we get
2secx = 1/√3 + √3 = 4/√3
secx = 2/√3
And, tanx = 2/√3 – 1/√3 = 1/√3
secx × tanx = 2/3
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