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

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Answer 1 · 2017-01-02T07:28:24

$(1+cosx)/(1+secx)=cosx$ and for $x=pi/3$ , it is $1/2$ .

$(1+cosx)/(1+secx)$

= $(1+cosx)/(1+1/cosx)$

= $(1+cosx)/((cosx+1)/cosx)$

= $(1+cosx)xxcosx/(1+cosx)$

= $cosx$

Hence $(1+cosx)/(1+secx)=cosx$ for all values of $x$

and for $x=pi/3$

$(1+cosx)/(1+secx)=(1+cos(pi/3))/(1+sec(pi/3))$

= $(1+1/2)/(1+2)=(3/2)/3=3/2xx1/3=1/2$

As $cosx=cos(pi/3)=1/2$

for $x=pi/3$ , $(1+cosx)/(1+secx)=cosx$

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