For \(\displaystyle{x}\in{\left({0},{\frac{{\pi}}{{{2}}}}\right)}\) find a minimal value, which

Saul Cochran

Saul Cochran

Answered question

2022-04-15

For x(0,π2) find a minimal value, which the expression
secx+cscx+sec2x+csc2x
can take.

Answer & Explanation

Zaria Lamb

Zaria Lamb

Beginner2022-04-16Added 8 answers

Let sinx=a and cosx=b
Hence, a2+b2=1 and by AM-GM we obtain:
secx+cscx+sec2x+csc2x=
=a+bab+1a2b222a2+b2+4(a2+b2)2=4+22
The equality occurs for a=b=12, which says that we got a minimal value.

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