What is the principal solution of cosx =1?please answer it . I am not getting it.

Ajay
209 Points
8 years ago
Principal values are generally referred to Range of Inverse Trignometric functions.
For arcos function the principal values are
Ajay
209 Points
8 years ago

Principal values are generally referred to Range of Inverse Trignometric functions. This is to restrict the range of inverse trinometric functions which can have many  values for a given value in its domain.

$For\quad example\quad { cos }^{ -1 }1\quad can\quad have\quad multiple\quad values\quad as\quad 0,\quad 2\pi \quad etc\quad which\quad makes\quad the\quad function\quad as\quad one\quad to\quad many.\\ but\quad a\quad function\quad cannnot\quad be\quad one\quad to\quad many\quad hence\quad we\quad need\quad to\quad restrict\quad the\quad range\quad of\quad function\quad and\quad this\quad range\quad \\ is\quad called\quad principal\quad vlaues\\ \\ For\quad { cos }^{ -1 }x\quad \quad principal\quad values\quad lies\quad in\quad interval\quad [-\pi ,\quad \pi ]\\ or\quad we\quad can\quad say\quad that\quad -\pi \quad \le { cos }^{ -1 }x\le \quad \pi \\ Using\quad this\quad information\quad we\quad can\quad say\quad cosx\quad =\quad 1\quad \\ or\quad x\quad =\quad { cos }^{ -1 }1\quad \\ x\quad =\quad \quad 0\quad since\quad x\quad lies\quad is\quad interval\quad for\quad principal\quad values$