Does the equation `2^(sin^2 x)+2^(cos^2 x)=1.5(tan x+cot x)` have any solutions ?

Solve the equation (tan x )^( cos^(2) x)= ( cot x )^( sin x )

Solve the equation (tan x )^( cos^(2) x)= ( cot x )^( sin x )

Solve the equation, (tan x)^(cos^2 x) = (cot x)^(sin x)

Solve the equation (tan x )^( cos^(2) x)= ( cot x )^( sin x )

Solve the equation (tan x )^( cos^(2) x)= ( cot x )^( sin x )

Solve the equation (tan x )^( cos^(2) x)= ( cot x )^( sin x )

For which values of a does the equation 4sin(x+pi/3)cos(x-pi/6)=a^2+sqrt(3)sin2x-cos2x have solution? Find the solution for a=0.

For which values of a does the equation 4sin(x+pi/3)cos(x-pi/6)=a^2+sqrt(3)sin2x-cos2x have solution? Find the solution for a-0.

Let alpha is the solution of equation sin^(-1)(2sin^(-1)(cos^(-1)(tan^(-1)x)))=0 and beta is the solution of equation sin^(-1)x+sin^(-1)x^(2)=(pi)/(2), then -

Does the equation [(x-2)^(2)+4]*[x+(1)/(x)]=81 have any real solution ?