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3.Trigonometrical Ratios, Functions and Identities
medium
If $\sin A,\cos A$ and $\tan A$ are in $G.P.$, then ${\cos ^3}A + {\cos ^2}A$ is equal to
A
$1$
B
$2$
C
$4$
D
None of these
Solution
(a) We have $\sin A,\,\cos A$ and $\tan A$ are in $G.P.$
${\cos ^2}A = \sin A\,\tan A = \frac{{{{\sin }^2}A}}{{\cos A}}\, $
$\Rightarrow \,{\cos ^3}A – {\sin ^2}A = 0$
Hence ${\cos ^3}A + {\cos ^2}A = {\sin ^2}A + {\cos ^2}A = 1$
Standard 11
Mathematics
