Maths-

General

Easy

Question

# If , then

- None of these

Hint:

### In this question, we have to find the k and K, we have given k ≤ sin^{-1}x + cos^{-1}x + tan^{-1}x ≤ K. Here, it is asking about the period of this function.

## The correct answer is:

### Here we have to find the range of function which , k and K.

Firstly, we have k ≤ sin^{-1}x+ cos^{-1}x +tan^{-1}x ≤ K

We can write,

sin^{-1}x + cos^{-1}x + tan^{-1}x = + tan^{-1}x [we know sin^{-1}x + cos^{-1}x = ]

since,

k ≤ + tan^{-1}x ≤ K

so , sin^{-1}x and cos^{-1}x only defined if -1 ≤ x ≤ 1

we know that,

() ≤ tan^{-1}x ≤()

() ≤ + tan^{-1}x ≤( )

() ≤ + tan^{-1}x ≤()

Therefore, k = and K =

The correct answer is None of these.

In this question, we have to find the range of function from k to K. Here we know that sin^{-1}x + cos^{-1}x = and it only defines if -1 ≤ x ≤ 1 . And tan^-1x lines in () to ( ) .

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