HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
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# Solution for In ΔABC, prove that : tan((a-b)/2)=(a-b)/(a+b) cotC/2 - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

ConceptTrigonometric Functions Solution of a Triangle

#### Question

In ΔABC, prove that : tan((a-b)/2)=(a-b)/(a+b)cotC/2

#### Solution

In ΔABC by sine rule, we have

a/sinA=b/sinB=c/sinC=k

a=ksinA,b=ksinB and c=ksinC

Now, consider

(a-b)/(a+b)=(ksinA-ksinB)/(ksinA+ksinB)

=(sinA-sinB)/(sinA+sinB)

=(2cos((A+B)/2).sin((A-B)/2))/(2sin((A+B)/2).cos((A-B)/2))

=cot((A+B)/2).tan((A-B)/2)

=cot(pi/2-C/2).tan((A-B)/2) .....[because A+B+C=pi]

=tan(C/2)tan((A-B)/2)

(a-b)/(a+b)=tan((A-B)/2)/cot(C/2)

tan((A-B)/2)=(a-b)/(a+b)cot(C/2)

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#### APPEARS IN

2014-2015 (October) (with solutions)
Question 2.2.2 | 4.00 marks
Solution In ΔABC, prove that : tan((a-b)/2)=(a-b)/(a+b) cotC/2 Concept: Trigonometric Functions - Solution of a Triangle.
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