Example 1
If A + B = 45°, then find the value of
equals
a)1
b)0
c)2
d)1
Let us first try to understand the question. It means that if A + B = 45°, then the value of
is always constant, which is equal to one of the options. So, for all combinations of angles A and B whose sum is 45°, the value of (
will always be the same, which is equal to one of the four options.
So, whether (A = 0° and B = 45°) or (A = 1 ° and B = 44°) or (A = 10° and B = 35°), they all will give the same value of (1+tanA)(1+tanB). So, we can easily replace A and B with some convenient values of angles and get the required value of (1+tanA) * (1+tanB). Let us put A = 0° and B = 45°,
= (1+tan0°)(1+tan45°) = (1 + 0)(1 + 1) = 1*2 = 2
So, option C is correct
Example 2


Now we have to select the option that gives the correct sum for all natural number values of n. So, the correct option has to be true for n = 1, 2, 3, …and all other natural number values of n. So, if any option is giving the wrong sum for n = 1, we can be sure that that option is incorrect.
Also Read,
Let us try to find the options that are incorrect.
For n = 1, the actual sum of the given series is
= 
Checking what value option A for n = 1:
. So, it gives the wrong answer for n = 1, and hence it cannot give the correct answer for all values of n. Hence this option is wrong.
Checking what value option B for n = 1: (
. So, it gives the correct answer for n = 1. But this might give wrong answers for higher values of n. So, we will not mark this as correct right now.
Checking what value option C for n = 1:
So, it gives the correct answer for n = 1. But this might give wrong answers for higher values of n. So, we will not mark this as correct right now.
Checking what value option D for n = 1:
So, it gives the wrong answer for n = 1, and hence it cannot give the correct answer for all values of n. Hence this option is wrong.
Now both options A and D are eliminated, and one of option B or C is correct. Let us now see which of these two is giving the correct answer for n = 2.
For n = 2, the actual sum of the given series is

Checking what value option B for n = 2:
. So, it gives the correct answer for n = 2 as well. But this might give wrong answers for higher values of n. So, we will not mark this as correct right now.
Checking what value option C for n = 2:
. So, it gives the wrong answer for n = 2, and hence it cannot give the correct answer for all values of n. Hence this option is wrong.
Now we know that 3 out of 4 options are wrong, and only option B is left. So, we can safely mark option B as correct.
Example 3

If the value of the determinant given equals ka3b3c3, then the value of k is
a)1
b)0
c)-1
d)2
This question means that the value of the determinant always equals ka3b3c3 for all sets of values of a, b and c. In such questions, we can substitute some values of a, b and c and check to see the values of the determinant and the value of ka3b3c3. Also try to keep values of a, b and c such that ka3b3c3 does not become 0. So we will keep non-zero values of a, b and c. Let us put a = b = c = 1.
The value of the determinant is

which equals 0 (As two columns are the same) and the value of ka3b3c3 is k. So comparing these, we get k = 0.
Know when to use this trick and when not to. Don't use it for questions with more than one right answer or for multiple-choice questions where 'None of these' or 'All of these' is the only correct option.