Question

If $sinA=\frac{3}{5}$ and $A$ is in first quadrant, then the values of $sin2A$, $cos2A$ and $tan2A$ are

• A. $24/25$, $7/25$, $24/7$
• B. $1/25$, $7/25$, $1/7$
• C. $24/25$, $1/25$, $24/7$
• D. $1/25$, $24/25$, $1/24$

Answer 1

Answer: (A)

We have, $sinA=\frac{3}{5}$
$\Rightarrow cosA=\sqrt{1-sin^{2}\,A}=\sqrt{1-\frac{9}{25}}$
$=\sqrt{\frac{16}{25}}=\frac{4}{5}$
and $tanA=\frac{sin\,A}{cos\,A}=\frac{3/5}{4/5}=\frac{3}{4}$
Now, $sin2A=2sinA\cdot cosA$
$=2\times\frac{3}{5}\times\frac{4}{5} =\frac{24}{25}$
$cos2A=1-2sin^{2}A=\frac{7}{25}$
and $tan2A=\frac{24}{7}$