Trigonometric Substitution for Inequality | Trig Sub for Inequality | Inequality | Trigonometry

Trigonometric Substitution for Inequality is shown in this video.

Trigonometric Substitution will make it possible for Algebra Proof cause
we can use the Properties of Trigonometric Functions to solve the proof.

Sin squared plus cos squared equals 1 is an important property of Trigonometric Functions. We will use this property to simplify the proof.

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The algebra proof is : a squared + 1 over a squared × b squared + 1 over b squared is greater than or equal to 25 over 4, if we know : a squared + b squared=1.

There is a squared + b squared=1 in the given condition, so we will use the trig sub: Sin squared plus cos squared equals 1.

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The algebra proof is solved by using Trigonometric Substitution in this video. It will be possible for us to solve some difficlute algebra problems if we can use Trigonometry Knowledge with flexibility.

#Trigonometry #Trigonometric Substitution #Trigonometric functions #Inequality

[zobkey]

We can also do the following :
b² = 1-a²
We subtitute it in the inequality, and call the function f(x)=(a²+1/a²)(1-a²+1/(1-a²))
By using the derivative we can find the min value.
Otherwise, trig sub is a superb method!