Trigonometric Identities Question 144
Question: If $ \sin A,\cos A $ and $ \tan A $ are in G.P., then $ {{\cos }^{3}}A+{{\cos }^{2}}A $ is equal to
Options:
A) 1
B) 2
C) 4
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
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 $
BETA
