help me to fine the value of x
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The value of x may be -2
rohitprodhan:
in this case you don't say the exact value (one) of x..
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cot2x=cosx+sinx
square both sides
cot^2 2x=1+sin2x
cos^2 2x=sin^2 2x(1+sin2x)
1-sin^2 2x=sin^2 2x + sin^3 2x
sin^3 (2x )+2sin^2 (2x) =1
let sin2x=t
T^3+2T^2-1=0...(1)
one solution is t=-1..find others by dividing (1) by (t+1)..
for T=-1
sin2x=-1
2x=3π/2
x=3π/4...and many others as it depends on quad
square both sides
cot^2 2x=1+sin2x
cos^2 2x=sin^2 2x(1+sin2x)
1-sin^2 2x=sin^2 2x + sin^3 2x
sin^3 (2x )+2sin^2 (2x) =1
let sin2x=t
T^3+2T^2-1=0...(1)
one solution is t=-1..find others by dividing (1) by (t+1)..
for T=-1
sin2x=-1
2x=3π/2
x=3π/4...and many others as it depends on quad
sin2x=-1....x=3π/4
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