Show that `2^( sinx)+2^(cos x) ge 2^(1-1/sqrt(2))` for all real x.

show that 2^(sin x)+2^(cos x)ge2^(1-(1)/sqrt(2))

The inequality 2^(sintheta)+2^(costheta)ge2^(1-1/sqrt(2)) ,holds for all real values of theta

Show that 1+x ln (x+sqrt(x^2+1))geqsqrt(1+x^2) for all xgeq0.

Show that 1+xin(x+sqrt(x^2+1))geqsqrt(1+x^2) for all xgeq0.

find all the possible triplets (a_(1), a_(2), a_(3)) such that a_(1)+a_(2) cos (2x)+a_(3) sin^(2) (x)=0 for all real x.

Prove that, (sin (x/2)-cos (x/2))^(2)=1-sinx

Show that(i) sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x ,-1/(sqrt(2))lt=xlt=1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^2))=2cos^(-1)x ,1/(sqrt(2))lt=xlt=1

int sinx sqrt(1-cos 2x) dx

f(x)=cos^(-1)(x^(2)/sqrt(1+x^(2)))

If x in (0, (pi)/(2)) , then show that cos^(-1) ((7)/(2) (1 + cos 2 x) + sqrt((sin^(2) x - 48 cos^(2) x)) sin x) = x - cos^(-1) (7 cos x)