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Answer 1 · 2017-12-01T18:24:16

# 1/2.#

We know that, #csc^2theta-cot^2theta=1.#

#:. (csctheta+cottheta)(csctheta-cottheta)=1.#

#:. (csctheta+cottheta)(1/sqrt3)=1...............[because," Given]."#

#:. csctheta+cottheta=sqrt3....................................................<<1>>.#

Also, #csctheta-cottheta=1/sqrt3......................[Given].............<<2>>.#

Then, #<<1>>+<<2>> rArr 2csctheta=sqrt3+1/sqrt3=4/sqrt3.#

#:. csc theta=2/sqrt3, &, <<1>> - <<2>>rArr cottheta=1/sqrt3.#

Hence, #costheta=costheta/sintheta*sintheta=cottheta*1/csctheta,#

#=1/sqrt3*sqrt3/2.#

# rArr costheta=1/2.#