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Prove the following identities (1-16) cosec x ( sec x - 1 ) - cot x ( 1 - cos x ) = tan x - sin x plixxxnmdjdkj

Prove the following identities (1-16)
cosec x (sec x-1)-cot x (1-cos x)=tan x-sin x
 
plixxxnmdjdkj

Grade:12

1 Answers

SJ
askIITians Faculty 97 Points
3 years ago
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LHS=cosecx(secx−1)−cotx(1−cosx)
=1/sinx(1/cosx−1)−cosx/sinx(1−cosx)
=1/sinx(1−cosx/(cosx) )−cosx/sinx(1−cosx)
=(1−cosx/sinx)(1/cosx−cosx)=(1−cosx)/(sinx)(1−cos2x/cosx)
=(1−cosx/sinx)(sin2x/cosx)
=(1−cosx)(sinx/cosx)
=sinx/cosx−sinx=tanx−sinx
=RHS
Henceproved
Thanks

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