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Answers
Answer:
The required numeric value of [ cot( 90 - A ) sin( 90 - A ) / sinA ] + [ cot40° / tan50° ] - ( cos^2 20° + cos^2 70° ) is 1
Step-by-step explanation:
Equation to be evaluated : [ cot( 90 - A ) sin( 90 - A ) / sinA ] + [ cot40° / tan50° ] - ( cos^2 20° + cos^2 70° )
From the properties of trigonometry :
cot( 90 - Ф ) = tanФ
sin( 90 - Ф ) = cosФ
= > [ tanA cosA / sinA ] + [ cot( 90 - 50 )° / tan50° ] - { cos^2 20° + cos^2( 90 - 20 )° }
= > [ tanA x ( cosA / sinA ) ] + [ tan50° / tan50° ] - { cos^2 20° + cos^2 ( 90 - 20 )° }
From the properties of trigonometry :
cosA / sinA = cotA = 1 / tanA
cos( 90 - Ф ) = sinФ
sin^2 Ф + cos^2 = 1
= > [ tanA x 1 / tanA ] + 1 - { cos^2 20° + sin^2 20° }
= > 1 + 1 - 1
= > 1
Hence the required numeric value of [ cot( 90 - A ) sin( 90 - A ) / sinA ] + [ cot40° / tan50° ] - ( cos^2 20° + cos^2 70° ) is 1
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