Cot Half Angle Formula

Trigonometry word comes from a Greek word trigon means – triangle and metron mean – to measure. Initially, was concerned with missing parts of the triangle’s numerical values and its computing, if the value of other parts were given.

Trigonometric functions include many formulas. Apart from trigonometric identities and ratios, there are other formulas like half angle formulas.

Multiple Formulas for Cot Half Angle

Half angle for Cotangent Cot theta/2 =Cosec theta + cot theta
Half angle for Cotangent (1 + cos theta) /sin theta
Half angle for Cotangent ±Sqrt (1+cos theta/1 – cos theta)
Half angle for Cotangent Sin theta/(1 – Cos theta)

Examples of Cot half-angle formulas

Question 1: What is the value of Cot x/2 if cosec x = 2/1 and cot x = 3 / 4?

Solution:

If cosec x = 2/1 and cot x = 3 / 4

Then, Cot theta/2 =Cosec theta + cot theta

= 2/1 + ¾

=(8+3)/4

= 11/4

Question 2: What is the value of Cot x/2 if sin x = 3/4 and cos x = 4/5 ?

Solution:

If sin x = 3/4 and cos x = 4/5

Then, Cot theta/2 = Sin theta/(1 – Cos theta)

= ¾ +(1- ⅘)

=15/4

Question 3: If the value of cos A = 7/25, then find the value of cot A/2.

Solution:
Given,
cos A = 7/25
\(cot \frac{A}{2}=\pm\sqrt{\frac{1+cos A}{1- cos A}}\\ =\pm \sqrt{\frac{1+\frac{7}{25}}{1-\frac{7}{25}}}\\ =\pm \sqrt{\frac{25+7}{25-7}}\) \(=\pm \sqrt{\frac{32}{18}}\\ =\pm \sqrt{\frac{16}{9}}\\=\pm \frac{4}{3}\)

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