Question

Prove that, sin 2x = 2tan x / 1+tan²x .​

Answer 1

Answer:

$by \: rhs \\ \frac{2 \tan(x) }{1 + { \tan }^{2} x} = \frac{2 \frac{ \sin(x) }{ \cos(x) } }{ \sec^{2} x} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \frac{ \sin(x) \sec(x) }{ \sec^{2} x} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \sin(x) \times \frac{1}{ \sec(x) } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \sin(x) \cos(x) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sin(2x) = lhs$

hope this will help u.....

Answer 2

Answer:

aa we know that 1 + tan^2x = sec^x

hence rhs= 2tanx/(sec^2x)

and 2tanx(cos^2x)

2(sinx/cosx)(cos^2x)

2sinxcosx

i.e sin2x

proved