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Pythagoras Theorem

32. SOLUTION ...

Question

32. SOLUTION OF TRIANGLES : In a triangle ABC, the angles A, B, C are in A.P. Show that :2cos [(A-C)/2] = (a+c)/sqrt(a²-ac+c²)

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A, B, C

A . P .

2 cos \frac{A - C}{2} = \frac{a + c}{\sqrt{(a^{2} - a c + c^{2})}}

△ A B C

cot A, cot B, cot C

a^{2}

, b^{2}, c^{2}

A B C

a, b, c

G . P .

sin A, sin B, sin C

A . P .,

△ A B C

a, b, c

units

△ A B C

∠ A, ∠ B

∠ C

△ A B C, c {cos}^{2} \frac{A}{2} + a {cos}^{2} \frac{C}{2} = \frac{3 b}{2},

a, b, c

△ A B C

△ A D C

∠ C A D = ∠ C B D

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