Question

2(1-sin^3x)÷
cos2^2x
lim
x=π÷2​

Answer 1

>>Applied Mathematics

>>Limits and Continuity

>>Properties of limits

>>The value of limit x→pi/21 - sin^3x/cos

Question

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The value of

x→π/2

lim

cos

2

x

1−sin

3

x

is

Easy

Solution

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Correct option is B)

x→π/2

lim

cos

2

x

1−sin

3

x

=

x→π/2

lim

1−sin

2

x

(1−sinx)(1+sinx+sin

2

x)

=

x→π/2

lim

(1−sinx)(1+sinx)

(1−sinx)(1+sinx+sin

2

x)

=

x→π/2

lim

1+sinx

1+sinx+sin

2

x

=

1+1

1+1+1

=

2

3