Trigonometric Identities Question 109
Question: The equation $ {{(a+b)}^{2}}=4ab{{\sin }^{2}}\theta $ is possible only when
Options:
A) $ 2a=b $
B) $ a=b $
C) $ a=2b $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ {{(a+b)}^{2}}=4ab{{\sin }^{2}}\theta $
$ \Rightarrow {{\sin }^{2}}\theta =\frac{{{(a+b)}^{2}}}{4ab}\le 1\Rightarrow {{(a+b)}^{2}}-4ab\le 0 $
$ \Rightarrow {{(a-b)}^{2}}\le 0\Rightarrow a=b. $
BETA
