What is $\frac{1 + cos x}{1 + sec x}$ $(1+cosx)/(1+secx)$ for $x = \frac{π}{3}$ $x=pi/3$ ?

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Answer 1 · 2017-01-02T07:28:24

$\frac{1 + cos x}{1 + sec x} = cos x$ $(1+cosx)/(1+secx)=cosx$ and for $x = \frac{π}{3}$ $x=pi/3$ , it is $\frac{1}{2}$ $1/2$ .

$\frac{1 + cos x}{1 + sec x}$ $(1+cosx)/(1+secx)$

= $\frac{1 + cos x}{1 + \frac{1}{cos x}}$ $(1+cosx)/(1+1/cosx)$

= $\frac{1 + cos x}{\frac{cos x + 1}{cos x}}$ $(1+cosx)/((cosx+1)/cosx)$

= $(1 + cos x) \times \frac{cos x}{1 + cos x}$ $(1+cosx)xxcosx/(1+cosx)$

= $cos x$ $cosx$

Hence $\frac{1 + cos x}{1 + sec x} = cos x$ $(1+cosx)/(1+secx)=cosx$ for all values of $x$ $x$

and for $x = \frac{π}{3}$ $x=pi/3$

$\frac{1 + cos x}{1 + sec x} = \frac{1 + cos (\frac{π}{3})}{1 + sec (\frac{π}{3})}$ $(1+cosx)/(1+secx)=(1+cos(pi/3))/(1+sec(pi/3))$

= $\frac{1 + \frac{1}{2}}{1 + 2} = \frac{\frac{3}{2}}{3} = \frac{3}{2} \times \frac{1}{3} = \frac{1}{2}$ $(1+1/2)/(1+2)=(3/2)/3=3/2xx1/3=1/2$

As $cos x = cos (\frac{π}{3}) = \frac{1}{2}$ $cosx=cos(pi/3)=1/2$

for $x = \frac{π}{3}$ $x=pi/3$ , $\frac{1 + cos x}{1 + sec x} = cos x$ $(1+cosx)/(1+secx)=cosx$

What is 1+cosx1+secx(1+cosx)/(1+secx) for x=π3x=pi/3?