1.

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»

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



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