Sine Half Angle Formula

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.

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


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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Practise This Question

There is a park with two triangular jogging tracks. Rahul and his friend Arjun went for jogging. The park had a route map which mentioned that the sides of jogging tracks with the same color have the same length and nothing was mentioned about different colored sides.

Which of the following is true?

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