Question

if sin A=3/5then find sin 2A​

Answer 1

Answer:

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TUSHAR CHANDRA

CERTIFIED EDUCATOR

We have sin a = 3/5

cos a = sqrt (1 - (sin a)^2)

=> sqrt (1 - 9/25)

=> sqrt (16/25)

=> 4/5 or -4/5 based on the value of a

sin 2a = 2*sin a*cos a

=> 2*3/5*4/5

=> 24/25 or -24/25 base on the angle a

Answer 2

Step-by-step explanation:

$\color{blue} \text{Solution : Given, \( \sin A=\frac{3}{5} \) and \( A \) is an acute angle} \\ \color{purple}\text{ Now, } \quad \cos ^{2} A=1-\sin ^{2} A=1-\frac{9}{25}=\frac{16}{25} \\ \color{orange}\therefore \quad \cos A=\frac{4}{5} \qquad \: \tt [ \because \: A \: is \: acute]$

$\color{red}\tt \text{Now,}\quad \sin 2 A=2 \sin A \cos A=2 \times \dfrac{3}{5} \times \dfrac{4}{5}=\dfrac{24}{25}$