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Bulgaria National Olympiad
1965 Bulgaria National Olympiad
Problem 2
trigonometric inequality with natural parameter
trigonometric inequality with natural parameter
Source: Bulgaria 1965 P2
June 23, 2021
inequalities
trigonometry
Problem Statement
Prove the inequality:
(
1
+
sin
2
α
)
n
+
(
1
+
cos
2
α
)
n
≥
2
(
3
2
)
n
(1+\sin^2\alpha)^n+(1+\cos^2\alpha)^n\ge2\left(\frac32\right)^n
(
1
+
sin
2
α
)
n
+
(
1
+
cos
2
α
)
n
≥
2
(
2
3
)
n
is true for every natural number
n
n
n
. When does equality hold?
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