Question

Show that lim θ→0 (1-cos2θ+ tan²θ)/θ sinθ = 3​

Answer 1

Answer:

(1-cos2θ+ tan²θ)/θ sinθ = 3

Answer 2

Answer:

lim

(1−cos2θ)

2

4θ(tanθ−sinθ)

=

θ→0

lim

(2sin

2

θ)

2

.cosθ

4θsinθ(1−cosθ)

=

θ→0

lim

sinθ.sin

2

θ.cosθ

θ.(1−cosθ)

=

θ→0

lim

sinθ

θ

×

θ→0

lim

sin

2

θ.cosθ.(1+cosθ)

(1−cosθ)(1+cosθ)

=

lim

θ→0

(

θ

sinθ

)

1

×

θ→0

lim

sin

2

θcosθ(1+cosθ)

(1−cos

2

θ)

=

1

1

×

θ→0

lim

sin

2

θ.cosθ(1+cosθ)

sin

2

θ

=

θ→0

lim

cosθ(1+cosθ)

1

=

2

1