If cosec A=√2find the value of 2 sin2A+3 cot2A4tan2A−co

If cosec A=√2find the value of 2 sin2A+3 cot2A4tan2A−co
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If cosec A=√2,find the value of 2 sin2A+3 cot2A4(tan2A−cos2A)

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SOLUTION

g i v e n space t h a t cos e c A equals square root of 2 t h e r e f o r e sin A equals fraction numerator 1 over denominator square root of 2 end fraction left square bracket b y space d r a w i n g space t r i g n o m e t r i c space t r a n g l e space b y space t h i s space a n g l e space A comma w e space g e t space h y p o t n u s e space square root of 2 space o p p o s i t e space 1 space s o space a d j a c e n t space 1 left parenthesis a s space square root of square root of 2 squared minus 1 end root right parenthesis s o sin A equals fraction numerator 1 over denominator square root of 2 end fraction rightwards double arrow sin squared A equals 1 half cos A equals fraction numerator 1 over denominator square root of 2 end fraction rightwards double arrow cos squared A equals 1 half tan A equals 1 rightwards double arrow c o t A equals 1 rightwards double arrow c o t squared A equals 1 n o w fraction numerator 2 sin squared A plus 3 c o t squared A over denominator 4 left parenthesis tan squared A minus cos squared A right parenthesis end fraction equals fraction numerator 2 cross times begin display style 1 half end style plus 3 cross times 1 over denominator 4 left parenthesis 1 minus begin display style 1 half end style right parenthesis end fraction equals fraction numerator 1 plus 3 over denominator 4 left parenthesis begin display style 1 half end style right parenthesis end fraction equals 4 over 2 equals 2

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