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Question

Write the equation of a tangent to the graphs of the following curves at the indicated points
y=sin2x at the point x=π12.

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Solution

To find : - equation of a tangent of y=sin2x at x=π12
y=sin(2x)

at x=π12

y=sin(2π12)=sinπ6=12
Now, y=2cos2x
at x=π12
y=2cos(π12)=2cosπ6=232
=3
slope=m=3
Use point - slope form
(yy0)=m(xx0)
where x0=π12,y0=12,m=3
(y12)=3(xπ12)
y=3x3π12+12
=3x+12(3π6+1).

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