Trigonometric Identities Question 239
Question: On simplifying $ \frac{{{\sin }^{3}}A+\sin 3A}{\sin A}+\frac{{{\cos }^{3}}A-\cos 3A}{\cos A}, $ we get
Options:
A) $ \sin 3A $
B) $ \cos 3A $
C) $ \sin A+\cos A $
D) 3
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{{{\sin }^{3}}A+\sin 3A}{\sin A}+\frac{{{\cos }^{3}}-\cos 3A}{\cos A} $
$ \Rightarrow \frac{{{\sin }^{3}}A+\sin A-4{{\sin }^{3}}A}{\sin A}+\frac{{{\cos }^{3}}A-[ 4{{\cos }^{3}}A-3\cos A ]}{\cos A} $
$ \Rightarrow \frac{3\sin A-3{{\sin }^{3}}A}{\sin A}+\frac{( -3{{\cos }^{3}}A+3\cos A )}{\cos A} $ $ =3-3{{\sin }^{2}}A-3{{\cos }^{2}}A+3 $ $ =6-3({{\cos }^{2}}A+{{\sin }^{2}}A) $ $ =6-3(1) $ $ =3 $
BETA
