if y=log(sinx),Show that y3=2cosxdividedby sin³x
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y = log(sinx)
differentiate with respect to x
dy/dx = y₁ = cosx/sinx = cotx
y₁ = cotx
again differentiate wrt x
y₂ = -cosec²x
again differentiate wrt x
y₃ = -(-2cosecx).(cosecx .cotx)
= 2cosec²x.cotx
= 2/sin²x . cosx/sinx
= 2cosx/sin³x
hence, y₃ = 2cosx/sin³x
differentiate with respect to x
dy/dx = y₁ = cosx/sinx = cotx
y₁ = cotx
again differentiate wrt x
y₂ = -cosec²x
again differentiate wrt x
y₃ = -(-2cosecx).(cosecx .cotx)
= 2cosec²x.cotx
= 2/sin²x . cosx/sinx
= 2cosx/sin³x
hence, y₃ = 2cosx/sin³x
madanrekha28:
tq
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