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In triangle PQR, p^2, q^2 \ and\ r^2 \ are\ in\ A.P. Then \cot P, \cot Q, \cot R \ are\ in

Option: 1

A.P.


Option: 2

G.P.


Option: 3

H.P.


Option: 4

None of these


Answers (1)

best_answer

\\p^2 ,q^2, r^2 \ are\ in\ A.P.\ \\ r^2-q^2=q^2-p^2\\ \sin ^2 R-\sin ^2 Q=\sin ^2 Q-\sin ^2 P\\ \sin (R+Q) \sin(R-Q)=\sin(Q+P)\sin (Q-P)\\ \sin(\pi-P)(\sin R \cos Q- \cos R \sin Q)=\sin(\pi-R)(\sin Q \cos P -\cos Q \sin P)\\ \sin(P)(\sin R \cos Q- \cos R \sin Q)=\sin(R)(\sin Q \cos P -\cos Q \sin P)\\ \text{divide both side by } \sin P \sin Q \sin R\\ \cot Q-\cot R=\cot P-\cot Q\\ \cot P,\cot Q,\cot R \ are\ in\ A.P.

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Anam Khan

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