Question

If sin 2A = 4/5, the value of tan A
when 0 <A < TI/4, is
a.
4/3
b. 3/4
c.
1/2
d. 3/5​

Answer 1

Answer:

Step-by-step explanation:

$\sin2A =\frac45\\\\\frac{2\tan A}{1+\tan^2 A}=\frac45\\\\4+4\tan^2A=10 \tan A\\\\4\tan^2A-10 \tan A+4=0\\\\4\tan^2A-8 \tan A- 2\tan A+4=0\\\\2\tan A( 2\tan A-4)-( 2\tan A-4)\\\\( 2\tan A-4)(2\tan A-1)=0\\\\tan A =2 \ Or \tan A=\frac12\\\\Given \ that \ 0 < A < \frac {\pi}4}, So \ \tan A \leq 1\\\\\bf \tan A= \frac12$