Question

if sec 2A = cosec (A - 42 degree) find A

Answer 1

Given Equation : sec 2A° = cosec ( A - 42 )°


There are two methods for the solution:


$\underline{\mathsf{Method 1 -}}$


From the properties of trigonometry, we know : -
SecA = cosec( 90 - A )


Now,
= > sec 2A = cosec( A - 42 )

= > sec 2A = cosec{ 90 - ( - A + 42 + 90 ) }

= > sec 2A = sec( - A + 42 + 90 )

= > sec 2A = sec ( - A + 132 )

= > 2A = - A + 132

= > 2A + A = 132

= > 3A = 132

= > A = 44




$\underline{\mathsf{Method 2 - }}$


From the properties of trigonometry, we know : -
cosecA = sec( 90 - A )


Then,
= > sec 2A = cosecA( A - 42 )

= > cosec( 90 - 2A ) = cosec( A - 42 )

= > 90 - 2A = A - 42

= > 90 + 42 = A + 2A

= > 132 = 3A

= > 44 = A




Hence,
Value of the used variable, A , is 44.
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