Trigonometric Equations Question 53
Question: If $ a^{2},b^{2},c^{2} $ are in A. P. then which of the following are also in A.P.
[ISM Dhandbad 1989]
Options:
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
Show Answer
Answer:
Correct Answer: C
Solution:
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$ {{\sin }^{2}}B-{{\sin }^{2}}A={{\sin }^{2}}C-{{\sin }^{2}}B $ \ $ \sin (B+A)\sin (B-A)=\sin (C+B)\sin (C-B) $ or $ \sin C(\sin B\cos A-\cos B\sin A) $ $ =\sin A(\sin C\cos B-\cos C\sin B) $ Divide by $ \sin A\sin B\sin C $
$ \therefore ,\cot A-\cot B=\cot B-\cot C $ . Hence the result.
BETA
