#y = sec^2theta + cos^2theta#, #theta != 0#, then?(Solve it without A.M - G.M inequality method)

Question

A: y #=# 0
B: y #<=# 2
C: y #>=# -2
D: y #># 2
The answer is (D) for your reference

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Answer 1 · 2017-08-02T14:10:49

#y>=2#

#y=sec^2theta+cos^2theta#

#=sec^2theta-2secthetacostheta+cos^2theta+2#

#=(sectheta-costheta)^2+2#

(as #2secthetacostheta=2#)

as #(sectheta-costheta)^2>=0#

#(sectheta-costheta)^2+2>=2#

i.e. #y=sec^2theta+cos^2theta>=2#