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If a^(2),b^(2),c^(2) are in AP, then whi...

If `a^(2),b^(2),c^(2)` are in AP, then which of the following is also an AP?

A

sin A , sin B,sin C

B

tan A,tanB,tanC

C

cot A, cotB, cotC

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
c
`sin^(2) B - sin^(2) A = sin^(2) C - sin^(2)B " " [ :. A^(2),b^(2),c^(2)` are in AP]
` rArr sin (B+A) sin (B-A) = sin (C+B)sin (C-B)`
` rArr sin C(sin B cos A - cos B sin A - cosB sin A)`
` = sin A( sin C cos B - cos C sin B) " " [ :' A+B+C = pi]`
` rArr 2 cot B = cot A + cot C ` [ divide by sin A sin B sin C]
Hence, cot A , cot B and cot C are in AP.
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