Let #E = √(1+sinA) + √(1-sinA).# If #0°<= A <= 90°# then find the find the value of E?

1 Answer
Oct 10, 2017

#E=2cos(A/2)#

Explanation:

#E=sqrt(1+sinA)+sqrt(1-sinA)#

#E^2=1+sinA+1-sinA+2sqrt[(1+sinA)*(1-sinA)]#

=#2+2sqrt[1-(sinA)^2]#

=#2+2sqrt[(cosA)^2]#

=#2+2cosA#

=#2*(1+cosA)#

=#2*2[cos(A/2)]^2#

=#4[cos(A/2)]^2#

Hence #E=2cos(A/2)#