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if,a2,b2,c2 are in AP, then which of the following is also in AP ?

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a
sin ⁡A,sin⁡ B,sin⁡ C
b
tan ⁡A,tan⁡ B,tan ⁡C
c
cot ⁡A,cot ⁡B,cot ⁡C
d
None of these

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detailed solution

Correct option is C

∵a2,b2,c2 are in AP.⇒ sin2 ⁡B−sin2 ⁡A=sin2 ⁡C−sin2 ⁡B⇒ sin ⁡C(sin⁡ Bcos ⁡A−cos ⁡Bsin ⁡A)=sin⁡ A(sin ⁡Ccos ⁡B−cos⁡ Csin ⁡B)On dividing by sin Asin B sin C, we get2cot ⁡B=cot ⁡A+cot⁡ C⇒ cot⁡A,cot⁡B,cot⁡C are in AP.


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