 # Law of tangent formula

Trigonometry includes angles and triangles. Trigonometric functions are:

• Sine,
• Cosine,
• Tangent,
• Cosecant,
• Secant,
• Cotangent.

The tangent( in trigonometry) is defined as an angle in a right-angled triangle which has a ratio of perpendicular and base. The tangent of an angle x is written as tan x.

The formula of a tangent in a right triangle PQR, where side opposite angle P, Q , R are p, q , r respectively.

 p-q/p+q ={ tan (P-Q)/2 }/{ tan (P+Q)/2} q-r/q+r ={ tan (Q-R)/2 }/{ tan (Q+R)/2} r-p/r+p ={ tan (R-P)/2 }/{ tan (R+P)/2}

## Example of Tangent Formula:

Problem : If in a triangle ABC, ∠B = 80∘∘, ∠C = 40∘∘. If the side opposite to ∠B is 4 cm. Find the value of side opposite to ∠C.

Solution:

b-c/b+c ={ tan (B-C)/2 }/{ tan (B+C)/2}

4-c/4+c ={ tan (80 – 40 )/2 }/{ tan (80 +40)/2}

4-c/4+c ={ tan 20 }/{ tan (60)}

4-c/4+c ={ 20 }/{ 60}

4-c/4+c =⅓

3(4-C) = 4 +C

12 -3C = 4 + C

12 – 4 = C +3C

8 = 4C

8/4 = C

C =2

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