#How do you prove it?

19 messages · Page 1 of 1 (latest)

elfin steepleBOT
agile lark
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I would use
$$\sqrt{\cos 70^{\circ}}>\sqrt{\cos 75^{\circ}}$$
and
$$\sqrt{\sin 70^{\circ}}>\sqrt{\sin 60^{\circ}}$$
If
$$\sqrt{\cos 75^{\circ}}+\sqrt{\sin 60^{\circ}}>1$$
then
$$\sqrt{\cos 70^{\circ}}+\sqrt{\sin 70^{\circ}}>1$$
by transitivity. Lastly $75^{\circ}=45^{\circ}+30^{\circ}$

hollow thicketBOT
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Crystopher

1013769549398671542.png
tight flame
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👏 , thanks

hollow thicketBOT
little cave
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I would just say that :

  1. (sinφ)² + (cosφ)² = 1
  2. When you square a number that's on interval (0;1), you make it smaller, so √sinφ will be bigger than sinφ.
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Thats all you need to prove that.

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So this mathematical equation is true for any angle φ:
√sinφ + √cosφ > 1

little cave
analog thistle
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I would suggest you to do

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AM greather than GM

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Arithmetic Mean and Geometric mean

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sin40 lies between 0 and 1

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to its 1/4th power

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will increase it

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hence we can conclude

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the Left hand side is greater than one

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if I am wrong, I want somebody to correct me