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Solution - In any ΔABC if  a2 , b2 , c2 are in arithmetic progression, then prove that Cot A, Cot B, Cot C are in arithmetic progression. - Trigonometric 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)
Question 2.2.2 | 4 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 Arts, HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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