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True :a cosec?a- acota |
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Answer» should I PROVE that cosec A - cotA= sinA/1+cosA?The solutions are :as cosec a=1/SIN aand cot a=cos a / sin aso , L.H.S. = cosec a - cot a = 1 /sin a - cos a/ sin a= (1-cos a) / sin a =(1- cos a)(1 + cos a) / sin a * (1 + cos a )=1 - cos^2 (a) / sin a *(1+ cos a) =sin ^2(a)/sin a * (1 + cos a)= sin a /(1 + cos a)= R.H.S.this is standard method to solve such problem , otherwise you can solve as2. as takingsin a =p/hcos a =b/hcosec a= h/ pcot =b /pwhere p,b,h are sides of a right angled triangle ,p=perpendicular sideb=base of the TRIANGLEH= hypotenuseput these valve in L.H.S. and R.H.S. and hence prove L.H.S. = R.H.S. .hope it will help |
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