Trigonometric Identities Question 343
Question: $ \frac{\sin 3\theta -\cos 3\theta }{\sin \theta +\cos \theta }+1= $
Options:
A) $ 2\sin 2\theta $
B) $ 2\cos 2\theta $
C) $ \tan 2\theta $
D) $ \cot 2\theta $
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ \frac{\sin 3\theta -\cos 3\theta }{\sin \theta +\cos \theta }=\frac{N}{D} $ (say) Then $ N=3\sin \theta -4{{\sin }^{3}}\theta -(4{{\cos }^{3}}\theta -3\cos \theta ) $ $ =3(\sin \theta +\cos \theta )-4({{\sin }^{3}}\theta +{{\cos }^{3}}\theta ) $ $ =(\sin \theta +\cos \theta ){3-4({{\sin }^{2}}\theta -\sin \theta \cos \theta +{{\cos }^{2}}\theta )} $
$ \therefore \ \frac{N}{D}+1= $ $ \frac{(\sin \theta +\cos \theta ){3-4(1-\sin \theta \cos \theta )}}{\sin \theta +\cos \theta }+1 $ $ =3-4(1-\sin \theta \cos \theta )+1 $ $ =4\sin \theta \cos \theta =2\sin 2\theta $ .
BETA
