if sec 2A = cosec (A - 42 degree) find A
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Given Equation : sec 2A° = cosec ( A - 42 )°
There are two methods for the solution:
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
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.
There are two methods for the solution:
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
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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