Good afternoon, students, welcome to the class. Today we will study inverse trigonometric functions

with respect to JEE Mains syllabus. We will solve those kinds of questions which come in JEE Mains.

Let us start with first very simple question. We have to find tan of cos inverse x.

See let cos inverse x is equal to theta, if cos inverse x is an angle equal to theta then x is equal to cos

theta, this means that x equals to cos theta. And we have to find tan of theta. If x is cos theta then

what will be tan theta is what we have to find out. If x is cos theta then what will tan theta be, we

have to find that out.

Simply speaking x is cos theta means if I take this as x and this as 1 then it will be cos theta, then this

will be 1 minus x square. So tan theta is equal to square root of 1 minus x square upon x. Using

simple triangles we can get the value of tan theta, square root of 1 minus x square upon x. I hope

everybody got it.

Second question is again very simple based on same thing, we have to find cos of 2 cos inverse 0.8. If

I take cos inverse 0.8 as theta then what will be cos theta, 0.8. I have to get cos 2 theta, what is cos 2

theta. 2 cos square theta minus 1, 2 into 0.8 into 0.8 minus 1. 2 into 0.64 minus 1 that is 0.64 into 2

is 1.28 minus 1 that is 0.28. Answer is 0.28 which is not in options so the answer is none of these.

Cos theta 0.8 is 2 cos square theta minus 1 that is 2 into 0.8 into 0.8 minus 1. Got it, very good.

Third question, similar questions are asked in school also. Let us apply tan inverse of x plus tan

inverse of y is equal to tan inverse of x plus y upon 1 minus xy. Because both these angles are less

than pi by 4, both are less than tan inverse, we can directly use this formula, this will become tan

inverse one by.