If sinθ+cosecθ=4 Then sin2θ-cosec2θ =?

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Answer 1 · 2018-04-27T06:45:37

The answer is #=-1.421#

#sintheta+csctheta=4#

#sintheta+1/(sintheta)=4#

#sin^2theta+1=4sintheta#

#sin^2theta-4sintheta+1=0#

Solving this quadratic equation in #sintheta#

#sintheta=(4+-sqrt((-)^2-4*1*1))/(2)=(4+-sqrt12)/2#

#sintheta=2+-sqrt3#

We keep only

#sintheta=2-sqrt3=0.268#

#theta=15.54^@#

So,

#sin(2theta)=sin (2*15.54^@)=0.516#

#1/sin(2theta)=1/0.516=1.937#

Finally,

#sin(2theta)-cosec(2theta)=sin(2theta)-1/sin(2theta)#

#=0.516-1.937=-1.421#