Prove that: (1 + 3sin A - 4 sin^3 A) / ( 1- sinA) =< (1 + 2sinA)^2

Answer:


These questions are a medium difficulty questions and you need to apply the mid term factorization method to solve these questions.

First we expand the middle term into two numbers so that when we multiply those two numbers together we get the product of first and the last term. And when we put the operator of the last term in between those numbers, we get the middle term.

Here, first term = 1
Middle term = 3
Last term = 4

We have,
Number1 * Number2 = first term* last term
Or, 4*1 = 1*4

And, we have operator '-'
So, number1 - number2 = middle term
       4-1= 3

So, we meet both the conditions when our first number is 4 and the second number is 1
Then we can expand the middle term.

Now, we can use the formula and factorization and canceling methods to prove as shown in the image above.

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