Question:
The value of sin (2 tan-1(0.75)) is equal to
(a) 0.75
(b) 1.5
(c) 0.96
(d) sin 1.5
Solution:
(c) 0.96
We have, sin (2 tan-1(0.75))
$=\sin \left(2 \tan ^{-1} \frac{3}{4}\right)=\sin \left(\sin ^{-1} \frac{2 \cdot \frac{3}{4}}{1+\frac{9}{16}}\right)\left(\because 2 \tan ^{-1} x=\sin ^{-1} \frac{2 x}{1+x^{2}}\right)$
$=\sin \left(\sin ^{-1} \frac{3 / 2}{25 / 16}\right)=\sin \left(\sin ^{-1} \frac{24}{25}\right)=\frac{24}{25}=0.96$
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