The value of sin 2 x is equal to (. where, .x ≠ n π+(π/2))

Question

The value of sin 2 x is equal to (. where, .x ≠ n π+(π/2)) (A) 2 sin x ⋅ cos x (B) (2 tan x/1+ tan 2 x) (C) Both (a) and (b) are true (D) None of the above

Tardigrade Admin · Accepted Answer

We have, sin (x+y)= sin x cos y+ cos x sin y On replacing y by x, we get sin 2 x=2 sin x cos x Again, sin 2 x=(2 sin x cos x/ cos 2 x+ sin 2 x) On dividing each term by cos 2 x, we get sin 2 x=(2 tan x/1+ tan 2 x)

Q. The value of $sin 2 x$ is equal to $($ where, $x \neq = nπ + \frac{π}{2})$

$2 sin x \cdot cos x$

$\frac{2 t a n x}{1 + t a n ^{2} x}$

Both (a) and (b) are true

None of the above

We have, $sin (x + y) = sin x cos y + cos x sin y$
On replacing $y$ by $x$ , we get
$sin 2 x = 2 sin x cos x$
Again, $sin 2 x = \frac{2 s i n x c o s x}{c o s ^{2} x + s i n ^{2} x}$
On dividing each term by $cos^{2} x$ , we get
$sin 2 x = \frac{2 t a n x}{1 + t a n ^{2} x}$

Q. The value of sin2x is equal to ( where, x=nπ+2π​)

2sinx⋅cosx

1+tan2x2tanx​