If secx - tanx = 1/√3, then the value of secx × tanx is:
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Correct answer: A
Explanation
Given:
secx − tanx = 1/√3
By the formula:
(secx − tanx)(secx + tanx) = 1
secx + tanx = 1 / (secx − tanx)
= 1 / (1/√3)
= √3
secx − tanx = 1/√3
secx + tanx = √3
2secx = √3 + 1/√3
= (3 + 1)/√3
= 4/√3
secx = 2/√3
2tanx = √3 − 1/√3
= (3 − 1)/√3
= 2/√3
tanx = 1/√3
secx × tanx = (2/√3) × (1/√3)= 2/3