HSC Science (General) 12th Board ExamMaharashtra State Board
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# Solution for In any ΔABC if  a2 , b2 , c2 are in arithmetic progression, then prove that Cot A, Cot B, Cot C are in arithmetic progression. - HSC Science (General) 12th Board Exam - Mathematics and Statistics

ConceptTrigonometric Functions Solution of a Triangle

#### Question

In any ΔABC if  a2 , b2 , c2 are in arithmetic progression, then prove that Cot A, Cot B, Cot C are in arithmetic progression.

#### Solution

Given that a2 ,b2 ,c2 are in arithmetic progression.
We need to prove that cotA, cotB and cotC are in
arithmetic progression.
a2 ,b2 ,c2 are in A.P.

-2a^2, -2b^2, -2c^2 " are in A.P"

(a^2+b^2+c^2)-2a^2,(a^2+b^2+c^2)-2b^2, (a^2+b^2+c^2)-2c^2 " are in A.P"

(b^2+c^2-a^2), (c^2+a^2-b^2),(a^2+b^2-c^2) " are in A.P "

(b^2+c^2-a^2)/(2abc), (c^2+a^2-b^2)/(2abc),(a^2+b^2-c^2) /(2abc)" are in A.P "

1/a(b^2+c^2-a^2)/(2bc), 1/b(c^2+a^2-b^2)/(2ac),1/c(a^2+b^2-c^2) /(2ab)" are in A.P "

1/acosA,1/bcosB,1/c cos C " are in A.P"

k/acosA,k/bcosB,k/c cos C " are in A.P"

cosA/sinA,cosB/sinB,cosC/sinC " are in A.P"

cotA,cotB,cotC " are in A.P"

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 2.2.2 | 4.00 marks
Solution for question: In any ΔABC if  a2 , b2 , c2 are in arithmetic progression, then prove that Cot A, Cot B, Cot C are in arithmetic progression. concept: Trigonometric Functions - Solution of a Triangle. For the courses HSC Science (General) , HSC Arts, HSC Science (Computer Science), HSC Science (Electronics)
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