Question #d6fb5

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Answer 1 · 2015-12-04T04:01:04

See explanation.

#[1]" "=csc(pi/12)#

Reciprocal Identity: #csctheta=1/sintheta#

#[2]" "=1/sin(pi/12)#

Represent #pi/12# as a difference of two special angles.

#[3]" "=1/sin((3pi)/12-(2pi)/12)#

#[4]" "=1/sin(pi/4-pi/6)#

Difference Identity: #sin(alpha-beta)=sinalphacosbeta-cosalphasinbeta#

#[5]" "=1/(sin(pi/4)cos(pi/6)-cos(pi/4)sin(pi/6))#

You can solve these since #pi/4# and #pi/6# are special angles.

#[6]" "=1/((sqrt2/2)(sqrt3/2)-(sqrt2/2)(1/2))#

#[7]" "=1/((sqrt6/4)-(sqrt2/4))#

#[8]" "=1/((sqrt6-sqrt2)/4)*4/4#

#[9]" "=4/(sqrt6-sqrt2)#

Rationalize the denominator.

#[10]" "=4/(sqrt6-sqrt2)*(sqrt6+sqrt2)/(sqrt6+sqrt2)#

#[11]" "=(4(sqrt6+sqrt2))/(6-2)#

#[12]" "=(cancel4(sqrt6+sqrt2))/cancel(4)#

#[13]" "=color(blue)(sqrt6+sqrt2)#