Question

Let f(x) = sin^-1x+cos^-1x. Then π/2 is equal to:

(a) f(-1/2)

(b) f(k²-2k+3), k belongs to R

(c) f(1/1+k²) ,k belongs to R

(d) f(-2)

Answer 1

Option (a) and (c) accepted

We know that for the relation

 sin^-1x+cos^-1x=π/2 , x€[-1,1]

As -1/2€[-1,1], f(-1/2)=π/2-> option (a)valid 

Now k²-2k+3=(k-1)²+2>2 for k€R

So ( k²-2k+3) does not belong to [-1,1]

Hence option (b) is not valid

Again 0<1/(1+k²) <1 for k€R

So (1/(1+k²)) € [-1,1] 

Hence option (c)  is valid.

As -2 does not belong to [-1,1]

Option (d) is not valid