Q)

Asked by araima2001 | 17th Jul, 2017, 10:00: AM

Expert Answer:

begin mathsize 16px style straight f left parenthesis straight x right parenthesis equals 5 sinx plus 12 cosx plus 14
As space square root of 5 squared plus 12 squared end root equals 13
rightwards double arrow straight f left parenthesis straight x right parenthesis equals 13 open parentheses 5 over 13 sinx plus 12 over 13 cosx close parentheses plus 14
Let space cos space straight beta equals 5 over 13 space and space sin space straight beta equals 12 over 13
rightwards double arrow straight f left parenthesis straight x right parenthesis equals 13 open square brackets sin open parentheses straight x plus straight beta close parentheses plus 14 close square brackets
sinx space to space be space one minus one
straight x element of open square brackets negative straight pi over 2 comma straight pi over 2 close square brackets
Range space open square brackets negative 1 comma 1 close square brackets
minus straight pi over 2 less or equal than straight x plus straight beta less or equal than straight pi over 2
rightwards double arrow negative straight pi over 2 minus straight beta less or equal than straight x less or equal than straight pi over 2 minus straight beta
tan space straight beta space equals 12 over 5 space space or space space straight beta equals tan to the power of negative 1 end exponent open parentheses 12 over 5 close parentheses
when space sin space open parentheses straight x plus straight beta close parentheses equals negative 1 space rightwards double arrow straight f left parenthesis straight x right parenthesis equals 1
sin space space open parentheses straight x plus straight beta close parentheses equals 1 space rightwards double arrow straight f left parenthesis straight x right parenthesis 27
one minus one space onto space when space minus straight pi over 2 minus straight beta less or equal than straight x less or equal than straight pi over 2 minus straight beta space and space
straight beta equals tan to the power of negative 1 end exponent open parentheses 12 over 5 close parentheses end style

Answered by Sneha shidid | 17th Jul, 2017, 10:59: AM