If the equation`2^((2pi)/cos^(-1)x)-(a+1/2)2^((pi)/cos^(-1)x-a^2=0` has exactly one real solution the range of `a` is equal to

If the equation2^((2pi)/cos^(-1)x)-(a+1/2)2^((pi)/cos^(-1)x-a^2=0 has exactly one real solution the range of a is equal to

If the equation sin^(-1)(x^(2)+x+1)+cos^(-1)(lambda x+1)=(pi)/(2) has exactly two solutions,then the value of lambda is

If the equation sin^(-1)(x^(2)+x+1)+cos^(-1)(lambda+1)=(pi)/(2) has exactly two solutions for lambda in[a,b], then the value of a+b is

tan((pi)/(4)+(1)/(2)cos^(-1)x)+tan((pi)/(4)-(1)/(2)cos^(-1)x),x!=0 is equal to

Q.if solution of the equation 2sin^(-1)x cos^(-1)x-2 pi sin^(-1)x-pi cos^(-1)x+pi^(2)=0 are alpha and beta such that then which of the following is lare correct?

The equation 2sin^(2)((x)/(2))*cos^(2)x=x+(1)/(x),0

If cos x=k has exactly one solutions in [0,2 pi], then write the values (s) of k