यदि ` sin A = (-4)/5 ` और` pi lt A lt (3pi)/2 ` तो ` ( "cosec" A + cot A)/( sec A - tan A)` का मान ज्ञात कीजिए ।

Explanation

` pi lt A lt (3pi)/2 rArr A ` तृतीय चतुर्थाश में है ।
` sin A = (-4)/5 `
` "cosec" A = 1/(sinA) = (-5)/4 `
` cot^(2) A = "cosec"^(2) A - 1 `
` = ((-5)/4)^(2) - 1 = 9/16`
` rArr cot A = 3/4 `
( तृतीय चतुर्थाश में cot धनात्मक होता है । )
` :. tan A = 1/ ( cot A ) = 4/3 `
` sec A = ( sin A ) / ( cos A ) * 1/( sin A) `
` = tan A * "cosec" A `
` = 4/3 ((-5)/4) = (-5)/3`
` ( "cosec" A + cot A ) /( secA - tan A) = ( (-5)/4+3/4)/((-5)/3 - 4/3 )= ((-2)/4)/((-9)/3 )= 1/6 `