Question

i am unable to get the point here, what's done​

Answer 1

Answer:

This and very similar kind of questions to this are some of the frequently asked questions in 10th class.

In the first step, both the denominator and numerator are divided by (cosθ)

whereas;

In the second step, both the numerator and denominator are multiplied with (tanθ–secθ).

And,

In the third step, the brackets are opened in the case of numerator only. Thus, applying the identity of

(a–b)(a+b)=a²–b²

• The denominator is left unsolved so as to cancel out it with the solved numerator.

Now, how do we get to know that with which term should we multiply or divide in each step!?

The answer is that this question has one hint (Which is given in the NCERT, but not in question papers or other sources).

i.e.,:– The question needs to be solved using an identity of (sec²θ=tan²θ+1).

So, to convert into such an RHS, we need to properly use this identity over here.

• Look, both the numerator and denominator are divided by cosθ, so as to get such an expression which contains only tanθ and secθ.

*Similar questions can be asked on the another two identities too.

E.g. If the question was based one cosecθ and cotθ, you'd need to divide both numerator and denominator by sinθ

You will get to know whatever is to be applied in various situations according to the question when you'll solve enough questions.

Keep Going and Keep practicing! :)