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Question
If x = a tan θ and y = b sec θ then
Options
`y^2/"b"^2 - x^2/"a"^2` = 1
`x^2/"a"^2 - y^2/"b"^2` = 1
`x^2/"a"^2 + y^2/"b"^2` = 1
`x^2/"a"^2 - y^2/"b"^2` = 0
Solution
`y^2/"b"^2 - x^2/"a"^2` = 1
Explanation;
Hint:
x = a tan θ
`x/"a"` = tan θ
`x^2/"a"^2` = tan2θ
`y^2/"b"^2 - x^2/"a"^2` = sec2θ – tan2θ = 1
y = b sec θ
`y/"b"` = sec θ
`y^2/"b"^2` = sec2θ
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Solution :
L.H.S. = cotθ + tanθ
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∴ cotθ + tanθ = cosecθ × secθ
