Question

find the value of sin2A when tanA=16/63

Answer 1

Given :

To find the value of Sin 2A when Tan A = $\frac{16}{63}$

Solution :

We know that,

Sin 2A = Sin (A + A) = Cos A Sin A + Sin A Cos A = 2 Sin A Cos A

Dividing & Multiplying by Cos A,

We get,

⇒ $Sin \ 2A =\frac{2 \ Sin \ A \ Cos \ A}{Cos \ A} \times Cos \ A$

⇒ $Sin \ 2A = 2 \ \frac{Sin \ A}{Cos \ A} Cos \ A \times Cos \ A$

⇒ $Sin \ 2A = 2 \ Tan \ A Cos^2A$

We know that,

$Cos \ A = \frac{1}{Sec \ A}$

So,

⇒ $Sin \ 2A = 2 \ Tan \ A (Cos \ A)^2$

⇒ $Sin \ 2A = \frac{2 \ Tan \ A}{Sec^2A}$

We know that,

Sec² A - Tan² A = 1

⇒ Sec² A = 1 + Tan² A

So,

⇒ $Sin \ 2A = \frac{2 \ Tan \ A}{Sec^2A}$

⇒ $Sin \ 2A = \frac{2 \ Tan \ A}{1+ \ Tan^2A}$

___

Substituting Tan A = $\frac{16}{63}$

We get,

⇒ $Sin \ 2A = \frac{2(\frac{16}{63})}{1+ (\frac{16}{63})^2}$

⇒ $Sin \ 2A = \frac{\frac{32}{63}}{1+ \frac{256}{3969}}$

⇒ $Sin \ 2A = \frac{\frac{32}{63}}{\frac{3969+256}{3969}}$

⇒ $Sin \ 2A = \frac{\frac{32}{63}}{\frac{4225}{3969}}$

⇒ $Sin \ 2A = \frac{\frac{32}{63}}{\frac{4225}{63 \times 63}}$

⇒ $Sin \ 2A = \frac{32 \times 63}{4225}$

⇒ $Sin \ 2A = \frac{2016}{4225}$

Answer 2

Answer:

tana=16/63

sin2a= 2tana/1+tan^2a( formula)

2×16/63

=----------------

1+(16/63)^2

32/63

= -------------------

1+ 256/3969

= 2016/4225

I hope you understand