Question

find the value of tan^-1(2sin(2cos1/2)))​

Answer 1

Answer:

First solve the inside bracket value 2cos

−1

2

3

The range of the principal value of cos

−1

x is [0,π]

Let cos

−1

2

3

=x

cosx=

2

3

x=

6

π

where x∈[0,π]

2cos

−1

2

3

=2

6

π

=

3

π

Then the expression reduces to tan

−1

(2sin

3

π

)

Now we are going to reduce the term 2sin

3

π

We know that sin

3

π

=

2

3

2sin

3

π

=2

2

3

=

3

The expression becomes, tan

−1

(

3

)

We know that tan

−1

(

3

)=

3

π

Therefore, tan

−1

[2sin(2cos

−1

2

3

)]=

3

π

.

Answer 2

Answer:

the answer is 3

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