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प्रश्न
The equation of normal to the curve y = tanx at (0, 0) is ______.
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उत्तर
The equation of normal to the curve y = tanx at (0, 0) is y + x = 0.
Explanation:
We have y = tan x.
So, `"dy"/"dx" = sec^2x`
∴ Slope of the normal = `(-1)/(sec^2x) = - cos^2x`
At the point (0, 0) the slope = `- cos^2(0)` = –1
So the equation of normal at (0, 0) is y – 0 = –1(x – 0)
⇒ y = – x
⇒ y + x = 0
Hence, the required equation is y + x = 0.
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