What is (1+cosx)/(1+secx)1+cosx1+secx for x=pi/3x=π3?

1 Answer
Jan 2, 2017

(1+cosx)/(1+secx)=cosx1+cosx1+secx=cosx and for x=pi/3x=π3, it is 1/212.

Explanation:

(1+cosx)/(1+secx)1+cosx1+secx

= (1+cosx)/(1+1/cosx)1+cosx1+1cosx

= (1+cosx)/((cosx+1)/cosx)1+cosxcosx+1cosx

= (1+cosx)xxcosx/(1+cosx)(1+cosx)×cosx1+cosx

= cosxcosx

Hence (1+cosx)/(1+secx)=cosx1+cosx1+secx=cosx for all values of xx

and for x=pi/3x=π3

(1+cosx)/(1+secx)=(1+cos(pi/3))/(1+sec(pi/3))1+cosx1+secx=1+cos(π3)1+sec(π3)

= (1+1/2)/(1+2)=(3/2)/3=3/2xx1/3=1/21+121+2=323=32×13=12

As cosx=cos(pi/3)=1/2cosx=cos(π3)=12

for x=pi/3x=π3, (1+cosx)/(1+secx)=cosx1+cosx1+secx=cosx