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Inverse Trigonometric Functions

Short Answer Type

31. Show that cos (sin–¹.x) = sin (cos^–1x) =

square root of 1 minus straight x squared end root space for space open vertical bar straight x close vertical bar space space less or equal than space 1

204 Views

32. If sin^–1x = y, then

(A) 0 ≥ y ≥

straight pi

(B)

negative straight pi over 2 less or equal than straight Y less or equal than straight pi over 2

straight pi

(D)

negative straight pi over 2 less than straight y less than straight pi over 2

265 Views

33.

tan to the power of negative 1 end exponent square root of 3 minus s e c to the power of negative 1 end exponent left parenthesis negative 2 right parenthesis

is equal

(A)

straight pi

(B)

negative straight pi over 3

(C)

straight pi over 3

(D)

fraction numerator 2 straight pi over denominator 3 end fraction

130 Views

34. Find the value of sin^–1

open parentheses sin space fraction numerator 3 straight x over denominator 5 end fraction close parentheses.

100 Views

35. Find the values of each of the expressions :

sin to the power of negative 1 end exponent open parentheses sin fraction numerator 2 straight pi over denominator 3 end fraction close parentheses

110 Views

36. Find the values of each of the expressions :

tan to the power of negative 1 end exponent open parentheses tan space fraction numerator 3 straight pi over denominator 4 end fraction close parentheses

108 Views

37.

Find the value of the following :

$cos to the power of negative 1 end exponent open parentheses cos space fraction numerator 13 straight pi over denominator 6 end fraction close parentheses$

109 Views

38.

Find the value of the following :

$tan to the power of negative 1 end exponent open parentheses tan space fraction numerator 7 space straight pi over denominator 6 end fraction close parentheses$

152 Views

39. Using principle value, evaluate the following :

cos to the power of negative 1 end exponent open parentheses cos fraction numerator 2 straight pi over denominator 3 end fraction close parentheses plus sin to the power of negative 1 end exponent open parentheses sin space fraction numerator 2 straight pi over denominator 3 end fraction close parentheses

133 Views

40. $If space sin open parentheses sin to the power of negative 1 end exponent 1 fifth plus cos to the power of negative 1 end exponent straight x close parentheses equals 1$ then find the value of x.

The given equation is

$space sin open parentheses sin to the power of negative 1 end exponent 1 fifth plus cos to the power of negative 1 end exponent straight x close parentheses equals 1 space space space space space space space space space space space space or space space sin to the power of negative 1 end exponent 1 fifth plus cos to the power of negative 1 end exponent straight x equals straight pi over 2 or space space sin to the power of negative 1 end exponent 1 fifth equals straight pi over 2 minus cos to the power of negative 1 end exponent straight x space space space space space space space space space space space space or space sin to the power of negative 1 end exponent 1 fifth equals sin to the power of negative 1 end exponent straight x rightwards double arrow space space space space space space space space straight x equals 1 fifth$