Home
Class 12
MATHS
If f(x)=sin^(-1)(sin x),g(x)=cos^(-1)(co...

If `f(x)=sin^(-1)(sin x),g(x)=cos^(-1)(cos x)` and `h(x)=cot^(-1)(cot x)`, then which of the following is/are correct ?

A

`f(x)=g(x)" if " x in (0, (pi)/(4))`

B

`f(x) lt g(x)" if " x in ((pi)/(2), (3pi)/(4))`

C

`f(x) lt g(x)" if " (pi, (5pi)/(4))`

D

`f(x) gt g(x)" if " x in (pi, (5pi)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNTIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-3 : Comprehension Type Problems|2 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Matching Type Problems|1 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|5 Videos

  • INDEFINITE AND DEFINITE INTEGRATION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|27 Videos

  • LIMIT

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|7 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=sin^(-1)x and g(x)=cos^(-1)x , then which of the following statements are correct?

If f(x) = sin^(-1) x. cos^(-1) x. tan^(-1) x . cot^(-1) x. sec^(-1) x. cosec^(-1) x , then which of the following statement (s) hold(s) good?

Let f:R->[-1, 1] be defined as f(x) = cos(sin x), then which of the following is(are) correct ?

Let f(x)=sin^(-1)x,g(x)=cos^(-1)x and h(x)=tan^(-1)x. For what complete interval of variation of x then following are true.

sin^-1(cos x)+tan ^-1(cot x)

Let f(x) = sin^(-1)|sin x| + cos^(-1)( cos x) . Which of the following statement(s) is / are TRUE ?

If f(x)=sin^(2)x, g(x)=sqrtx and h(x)=cos^(-1)x, 0 le xle 1, then

If f(x)=sin^(-1)(cosec(sin^(-1)x))+cos^(-1)(sec(cos^(-1)x)) , then f(x) takes

Let f(x)=(sin^(-1)x)/(cos^(-1)x)+(cos^(-1)x)/(tan^(-1)x)+(tan^(-1)x)/(sec^(-1)x)+(sec^(-1)x)/(cosec^(-1)x)+(cosec^(-1)x)/(cot^(-1)x)+(cot^(-1)x)/(sin^(-1)x) . Then which of the following statements holds good?

Let P(x)=cot^(2)x ((1+tanx+tan^(2)x)/(1+cot x+ cot^(2)x))+((cos x-cos 3x+sin3x-sin x)/(2(sin 2x+cos2x)))^(2) . Then, which of the following is (are) correct ?