Question 1189942

3.

given: 

{{{cos(x )= 2sin(x)}}},  in interval {{{0}}}°≤{{{x}}}<{{{360}}}°

{{{cos(x )= 2sin(x)}}}........both sides divide by {{{cos(x )}}}

{{{1= 2sin(x)/cos(x )}}}

{{{1/2= sin(x)/cos(x )}}}.....use identity

{{{tan(x)=1/2}}}

{{{x=tan^-1(1/2)}}}

{{{x=0.46364}}} radians

{{{x=26.57}}}°


Solutions for the range  {{{0}}}°≤{{{x}}}<{{{360}}}°:

{{{x=0.46364}}} radians
{{{x=0.46364 +pi}}}

{{{x= 26.57}}}°
{{{x=26.57+180=206.57}}}°



4.

{{{sec(x)/(1+sec(x)) = sec^2(x)/(2+sec(x))}}}.........cross multiply

{{{(2+sec(x))sec(x)= sec^2(x)(1+sec(x)) }}}

{{{2sec(x)+sec^2(x)= sec^2(x)+sec^3(x)}}}.......simplify 

{{{2sec(x)= sec^3(x)}}}..........simplify

{{{2= sec^2(x)}}}

{{{sec(x)=sqrt(2)}}}

{{{x=sec^-1(sqrt(2))}}}

{{{x=pi/4}}}}

{{{x=45}}}°


Solutions for the range {{{0}}}°≤{{{x}}}<{{{360}}}°:

Radians:

{{{x=pi/4}}}
{{{x=3pi/4}}}
{{{x=5pi/4}}}
{{{x=7pi/4 }}}

Degrees:

{{{x=45}}}°
{{{x=135}}}°
{{{x=225}}}°
{{{x=315}}}°