The expression- sin x - sin 2x1 - cos x - cos 2x- where x - - -2-2- lies in the interval

The correct option is B ( ∞ ,∞) →sin x+2 sin xcos x 1+cos x+2cos^ 2 x 1 →sin x( 1+2cos x ) #160; cos x( 1+2cos x ) #160; →tan x for ...

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Standard XII

Mathematics

Domain

The expressio...

Question

The expression, $\frac{sin x + sin 2 x}{1 + cos x + cos 2 x^{'}}$ where $x \in (- \frac{π}{2}, \frac{π}{2}),$ lies in the interval

(- \infty, \infty)

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(- 2, 2)

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(0, \infty)

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(- 1, 1)

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Solution

The correct option is B $(- \infty, \infty)$
$\to \frac{sin x + 2 sin x cos x}{1 + cos x + 2 {cos}^{2} x - 1}$
$\to \frac{sin x (1 + 2 cos x)}{cos x (1 + 2 cos x)}$
$\to tan x$
for $x ϵ (- π / 2, π / 2)$
$tan x ϵ (- \infty, \infty)$

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The expression, sinx+sin2x1+cosx+cos2x′ where x∈(−π2,π2), lies in the interval

The correct option is B (−∞,∞)→sinx+2sinxcosx1+cosx+2cos2x−1→sinx(1+2cosx)cosx(1+2cosx)→tanxfor xϵ(−π/2,π/2)tanxϵ(−∞,∞)

The expression, $\frac{sin x + sin 2 x}{1 + cos x + cos 2 x^{'}}$ where $x \in (- \frac{π}{2}, \frac{π}{2}),$ lies in the interval

The correct option is B $(- \infty, \infty)$
$\to \frac{sin x + 2 sin x cos x}{1 + cos x + 2 {cos}^{2} x - 1}$
$\to \frac{sin x (1 + 2 cos x)}{cos x (1 + 2 cos x)}$
$\to tan x$
for $x ϵ (- π / 2, π / 2)$
$tan x ϵ (- \infty, \infty)$