That's what typeof is there for. The parentheses are optional since it is an operator.

if (typeof variable == "boolean") {
    // variable is a boolean
}

With pure JavaScript, you can just simply use typeof and do something like typeof false or typeof true and it will return "boolean"...

But that's not the only way to do that, I'm creating functions below to show different ways you can check for Boolean in JavaScript, also different ways you can do it in some new frameworks, let's start with this one:

function isBoolean(val) {
   return val === false || val === true;
}

Or one-line ES6 way ...

const isBoolean = val => 'boolean' === typeof val;

and call it like!

isBoolean(false); //return true

Also in Underscore source code they check it like this(with the _. at the start of the function name):

isBoolean = function(obj) {
   return obj === true || obj === false || toString.call(obj) === '[object Boolean]';
};

Also in jQuery you can check it like this:

jQuery.type(true); //return "boolean"

In React, if using propTypes, you can check a value to be boolean like this:

MyComponent.propTypes = {
  children: PropTypes.bool.isRequired
};

If using TypeScript, you can use type boolean also:

let isDone: boolean = false;

Also another way to do it, is like converting the value to boolean and see if it's exactly the same still, something like:

const isBoolean = val => !!val === val;

or like:

const isBoolean = val => Boolean(val) === val;

and call it!

isBoolean(false); //return true

It's not recommended using any framework for this as it's really a simple check in JavaScript.

If you just want to check for a primitive value

typeof variable === 'boolean'

If for some strange reason you have booleans created with the constructor, those aren't really booleans but objects containing a primitive boolean value, and one way to check for both primitive booleans and objects created with new Boolean is to do :

function checkBool(bool) {
    return typeof bool === 'boolean' || 
           (typeof bool === 'object' && 
            bool !== null            &&
           typeof bool.valueOf() === 'boolean');
}

function checkBool(bool) {
    return typeof bool === 'boolean' || 
           (typeof bool === 'object' && 
            bool !== null            &&
           typeof bool.valueOf() === 'boolean');
}

console.log( checkBool( 'string'          )); // false, string
console.log( checkBool( {test: 'this'}    )); // false, object
console.log( checkBool( null              )); // false, null
console.log( checkBool( undefined         )); // false, undefined
console.log( checkBool( new Boolean(true) )); // true
console.log( checkBool( new Boolean()     )); // true
console.log( checkBool( true              )); // true
console.log( checkBool( false             )); // true