# Tutor profile: Harshit M.

## Questions

### Subject: Trigonometry

$$ Prove $$ $$ 4\sin(x)\cos(x) = \sin(4x) / \cos(2x) $$

sin(2x) = 2 sin(x) cos(x) = >(4x) = 2 \sin(2x) cos(2x) in the right hand side of the given identity. sin(4x) / cos(2x) = 2 sin(2x) cos(2x) / cos(2x) = 2 sin(2x) = 2 [ 2 sin(x) cos(x)] = 4 sin(x) cos(x) which is equal to the right hand side of the given identity

### Subject: Chemical Engineering

The humidity at dry-bulb temperature of 20oC is 30% and the humidity at dry-bulb temperature of 22oC is 24%, what is the slope of adiabatic cooling line? a) -0.01 b) -0.02 c) -0.03 d) -0.05

Slope of adiabatic cooling line = (0.3 – 0.24)/(20 – 22) = -0.03.

### Subject: Algebra

Simplify the following expressions and write them with positive exponents. $$ ( x y^{2})^{2} (x^{2} y^{2})^{2} / ( x y )^{4} $$

$$( x^{2} y^{4} ) ( x^{4} y^{4} ) / ( x^{4} y^{4}) = x^{6} y^{8} / ( x^{4} y^{4}) = x^{2} y^{4}$$

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