Trigonometric Equations Question 201
Question: In a $ \Delta ABC,a^{2}\sin 2C+c^{2}\sin 2A= $
[EAMCET 2001]
Options:
A) $ \Delta $
B) $ 2\Delta $
C) $ 3\Delta $
D) $ 4\Delta $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ a^{2}\sin 2C+c^{2}\sin 2A $ $ =a^{2}(2\sin C\cos C)+c^{2}(2\sin A\cos A) $ $ =2a^{2}( \frac{2\Delta }{ab}\cos C )+2c^{2}( \frac{2\Delta }{bc}\cos A ) $ $ (\because ,\Delta =\frac{1}{2}ab\sin C=\frac{1}{2}bc\sin A,,\therefore ,\sin C=\frac{2\Delta }{ab},,\sin A=\frac{2\Delta }{bc}) $ = $ 4\Delta { \frac{a\cos C+c\cos A}{b} }=4\Delta ( \frac{b}{b} )=4\Delta $ .
BETA
