Inverse Trigonometric Functions Exercise 2.1 Intro | Class 12 | Bihar & UP Board in English Medium

Transformations of inverse trigonometric functions need to be handled with care. Consider the identity sin2theta=(2tantheta)/(1+tan^2theta) in its domain of definition. Suppose we set tantheta=x , we have sin2theta=(2x)/(1+x^2) Taking sin^(-1) of both sides yields 2theta=sin^(-1).(2x)/1+x^2i.e.,2tan^(-1)x=sin^(-1).(2x)/(1+ x^2) . But we will discover that the above identity is not valid for all x. Choose x=sqrt3, LHS =2tan^(-1)sqrt3=2xxpi/3=(2pi)/3, RHS=sin.(2sqrt3)/(1+3)=sin^(-1).(sqrt3)/2=pi/3 . And so left hand and right hand side don't match. The reason is that we have disregarded the principal values of inverse functions. So it is well to remember that the iverse trigonometric formmulae have restrictions attached to the argument. When the values of x lie outside the interval of validity then the formula needs to be corrected. Let f(x)=sin^(-1)(x)/(1+x^2),g(x)=2tan^(-1)x . Then the largest interval in R on which f and g both are agree

If alpha=3sin^-1(6/11) and beta=3cos^-1(4/9) , where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)

If int(dx)/(x^2+a x+1)=f(g(x))+c , then f(x) is inverse trigonometric function for |a|>2 f(x) is logarithmic function for |a| 2 g(x) is rational function for |a|<2

Find the value of the other five trigonometric functions : cot theta = -12/5 , pi/2 lt theta lt pi

class 10 exercise 8.4 question 4 part 1and2

Find the value of other five trigonometric function cosx=-1/2, x lies in third quadrant.

If we consider only the principal values of the inverse trigonometric functions , then the value of tan(cos^-1 (1/(5sqrt2)) -sin^-1 (4/sqrt(17))) is (a) sqrt(29)/3 (b) 29/3 (c) sqrt3/29 (d) 3/29

Convert the trigonometric function sin[2cos^-1{cot(2tan^-1 x)}] into an algebraic function f(x). Then from thealgebraic functionfind all the values of x for which f(x) is zero. Express the values of x in the form a+-sqrt(b) where a and b are rational numbers.

Sentence : Type & Parts || Day 1 || Class 10 English Grammar || UP Board Exam 2022

Find the values of the other five trigonometric functions in each of the following: costheta=-1/2,theta in quadrant II