What is the equation of the line tangent to #f(x)=cos x + sin^2 x # at #x=0#?

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Answer 1 · 2016-01-05T19:54:20

#y = 1#

#f(x) = cos x + sin^2x #

#f'(x) = - sinx + 2sinx ( cosx) = 2sinxcosx - sinx#

at #x = 0#:

#f'(0) = 2sin0 cos0 - sin0 = 0#

now since the slope of the tangent line #= 0# the tangent will be parallel to the #x#-axis with the equation #y = k# where #k# is a constant.

#f(0) = cos 0 +(sin0)^2 = 1#

# rArr y=1 # is the equation of the line tangent.