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Mathematics

Half-Angle Formulae in Trigonometry

Gk Scientist March 12, 2022 No Comments
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Half-Angle Formulae in Trigonometry:

(i) In △ABC with BC = a, CA = b and AB = c,

half angle formulae for sin - Half-Angle Formulae in Trigonometry

The other two formulae can also be deduced similarly.

(ii) In △ABC with BC = a, CA = b and AB = c,

Half angle formulae for cos - Half-Angle Formulae in Trigonometry

The other two formulae can also be deduced in the same manner.

(iii) In △ABC with BC = a, CA = b and AB = c,

Half angle Formulae for tan - Half-Angle Formulae in Trigonometry

Similarly, the other two of the set can also be deduced.

half angle formulae - Half-Angle Formulae in Trigonometry

Example- In any △ABC, prove that bc cos2 (A/2) + ca cos2 (B/2) + ab cos2 (C/2) = s2, where 2s = a + b + c.

Solution:

bc cos2 (A/2) + ca cos2 (B/2) + ab cos2 (C/2)
= bc. s(s – a)/bc + ca. s(s – b)/ca + ab. s(s – c)/ab
= s(s – a) + s(s – b) + s(s – c)
= 3s2 – s(a + b + c) = 3s2 – s . 2s = 3s2 – 2s2 = s2

The Sine FormulaDual Nature of Radiations and Matter
The Cosine FormulaeDerivation of de-Broglie equation
Projection Formulae and Area of a TriangleHeisenberg Uncertainty Principle
Graphical Solution of Trigonometric EquationMagnetism and Electromagnetism– Tamil Board
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