2sin^2π/6+cosec^2×7×π/6×cos^2π/3=3/2
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HOMEWORK HELP > MATH
Find the value of 2sin^(2)pi/6 + cosec^(2) 7pi/6 cos^(2) pi/3?
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GSENVIRO eNotes educator| CERTIFIED EDUCATOR
Using the identity, cosec x =1/sin x , we get
2 sin^2 (pi/6) + (cos^2 (pi/3)) /(sin^2(7pi/6))
using the identity, sin (u+v) = sin u cos v +- cos u sin v
and writing 7pi/6 as (pi + pi/6), we get
2 sin^2(pi/6) + (cos^2(pi/3))/[sin pi cos (pi/6) +- sin (pi/6) cos pi]^2
using the values of sin and cos as sin (pi/6) = 1/2; cos (pi/3) = 1/2; sin pi = 0; cos pi = -1; we get
2 (1/2)^2 + [(1/2)^2]/[-+ 1/2]^2 = 2/4 + (1/4)/(1/4) = 3/2
Search for any book or any question
HOMEWORK HELP > MATH
Find the value of 2sin^(2)pi/6 + cosec^(2) 7pi/6 cos^(2) pi/3?
print Print document PDF list Cite
Expert Answers
GSENVIRO eNotes educator| CERTIFIED EDUCATOR
Using the identity, cosec x =1/sin x , we get
2 sin^2 (pi/6) + (cos^2 (pi/3)) /(sin^2(7pi/6))
using the identity, sin (u+v) = sin u cos v +- cos u sin v
and writing 7pi/6 as (pi + pi/6), we get
2 sin^2(pi/6) + (cos^2(pi/3))/[sin pi cos (pi/6) +- sin (pi/6) cos pi]^2
using the values of sin and cos as sin (pi/6) = 1/2; cos (pi/3) = 1/2; sin pi = 0; cos pi = -1; we get
2 (1/2)^2 + [(1/2)^2]/[-+ 1/2]^2 = 2/4 + (1/4)/(1/4) = 3/2
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