In some special cases where we add or subtract formulas for sine and cos, we get what is called as double-angle identities and half- angle identities. These half angle formulas let the trigonometric functions expressions of angles equate to x/2 in terms of x which can be later to functions and it would be easier to perform the complex calculations.
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Sin x/2 = ±√(1-cosx)/2 |
Practice questions on Sin x/2 Formula
Question: Find the value of sin 105 degrees using Sin half-angle formulas
Solution:
Sin 105 degree = sin 210 degree/2
Sin 105 degree = √(1 – cos 2100 )/ 2
= √(1 – (- cos 300)) / 2
= √(1 – (-√3/2)) / 2
= √(2 + √3) / 4
= √ (2 + √3) / 2
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