Answer The Value? 96Sin65° Sin35° Sin80°/Sin20° +2Sin80° Cos30°

Question

Answer The Value?
#(96Sin65° Sin35° Sin80°)/(Sin20° +2Sin80° Cos30°)#

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Answer 1 · 2018-05-21T06:19:12

# 24.#

Here, #"the Nr."=96sin65^@sin35^@sin80^@#,

#=48{2sin65^@sin35^@}sin80^@#,

#=48{cos(65^@-35^@)-cos(65^@+35^@)}sin80^@#,

#=48{cos30^@-cos100^@}sin80^@#,

#=48{sqrt3/2-cos(180^@-80^@)}sin80^@#,

#=48{sqrt3/2-(-cos80^@)}sin80^@#,

#=24sqrt3+48cos80^@sin80^@#,

#=24sqrt3+24(2cos80^@sin80^@)#,

#=24sqrt3+24sin(2xx80^@)#,

#=24(sqrt3+sin160^@)#,

#=24{sqrt3+sin(180^@-20^@)}#,

#rArr" Nr."=24(sqrt3+sin20^@)#.

Further, #"the Dr."=sin20^@+2sin80^@cos30^@#,

#=sin20^@+2*sin80^@*sqrt3/2#,

#=sin20^@+sqrt3sin80^@#.

Henc, #"the reqd. Value of the Exp.=(Nr.)/(Dr.)="24#.