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Question

To verify that the values of trigonometric ratios of an angle do not vary with the lengths of the sides of the triangle.

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Solution

Let's consider a triangle ABC with side vector a and bUsing dot product
ab=|a||b|cosθ
cosθ=ab|a||b|
=^a^b
Clearly cosθ is independent of |a|, it only depends on unit vector along CB and CA.

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