Solve sin 2x-5cos x-5sin x-1-0

Question

Toppr Admin · Accepted Answer

1-sin2x-sinx-cosx-2-x2234-u2-5u-0-x2234-u-0-x2212-5- -x2234-u-0-x21D2-tanx-x2212-1-x2234-x-n-x3C0-x2212-x3C0-4u-x2212-5 i-e- sinx-cosx-x2212-5 -not possible-

Solve $sin 2 x + 5 cos x + 5 sin x + 1 = 0$

$1 + sin 2 x = (sin x + cos x)^{2}$
$∴ u^{2} + 5 u = 0$
$∴ u = 0, - 5$ , $∴ u = 0 \Rightarrow tan x = - 1$
$∴ x = n π - \frac{π}{4}$
$u = - 5$ i.e., $sin x + cos x = - 5$ (not possible).

Solve sin2x+5cosx+5sinx+1=0

1+sin2x=(sinx+cosx)2∴u2+5u=0∴u=0,−5, ∴u=0⇒tanx=−1∴x=nπ−π4u=−5 i.e., sinx+cosx=−5 (not possible).

Solve $sin 2 x + 5 cos x + 5 sin x + 1 = 0$

$1 + sin 2 x = (sin x + cos x)^{2}$
$∴ u^{2} + 5 u = 0$
$∴ u = 0, - 5$ , $∴ u = 0 \Rightarrow tan x = - 1$
$∴ x = n π - \frac{π}{4}$
$u = - 5$ i.e., $sin x + cos x = - 5$ (not possible).