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

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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"`

 

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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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