# Tutor profile: Amal R.

## Questions

### Subject: Trigonometry

Prove that $$\frac{tan A+ Sec A-1}{tan A-Sec A+1}$$=$$\frac{1+Sin A}{Cos A}$$

$$ L.H.S$$ =$$\frac{tan A+ Sec A-1}{tan A-Sec A+1}$$ = $$\frac{tan A+ sec A-(sec^2A - tan^2 A)}{tan A-Sec A+1}$$ = $$\frac{(tan A +sec A) - ((sec A + tan A)(sec A - tan A)}{1-sec A+ tan A}$$ = $$\frac{(sec A+tan A)(1-sec A+tan A)}{1-sec A+tan A}$$ = $$ sec A+tan A $$ =$$\frac{1}{cos A}$$+$$\frac{1+sin A}{cos A}$$ = $$RHS$$

### Subject: Basic Math

The sum of three times a number and 2 less than 4 times that same number is 47. Determine the value of that unknown number.

$$3n+(4n-2) = 47$$ $$ 7n-2 = 47$$ $$ 7n = 47+2=49$$ $$ n = 49/7 =7$$

### Subject: Mechanical Engineering

Explain the following terms associated with a mechanism. (i) Limit Positions (ii) Dead Center

(i) It is the position of a mechanism when the interior angle between the crank and connecting rod is either 180 degree or 360 degrees. At these positions, large output torque can be generated by providing smaller input torque and hence the mechanical advantage tends to be infinity. (ii) It is the position of a mechanism when the interior angle between the connecting rod and follower is either 180 degree or 360 degrees.