SOLUTION: prove this identity (5 marks):
sin(x) + sin(x)cot(x)^2 = csc(x)
thanks in advance!
Algebra.Com
Question 199577: prove this identity (5 marks):
sin(x) + sin(x)cot(x)^2 = csc(x)
thanks in advance!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
 + \sin(x)\cot^2(x) = \csc(x))
... Start with the given equation.
\left(1 + \cot^2(x)\right) = \csc(x))
... Factor out the GCF
\csc^2(x) = \csc(x))
... Replace the terms in the parenthesis with )
.
Note: =\csc^2(x))
\left(\frac{1}{\sin^2(x)}\right) = \csc(x))
... Use the identity =\frac{1}{\sin(x)})
}{\sin^2(x)} = \csc(x))
... Multiply
}{\sin(x)\ast\sin(x)} = \csc(x))
... Factor
} = \csc(x))
... Cancel out the common terms.
 = \csc(x))
... Use the identity
So we've proven the identity.
RELATED QUESTIONS
Prove this identity.... (answered by Alan3354)
prove trigonometric identity (csc^2(x)-1)(sin(x))=... (answered by lwsshak3)
Prove the identity:... (answered by Edwin McCravy)
prove trigonometric identity for... (answered by lwsshak3)
Prove the identity csc x- cot x= sin x/1+ cos... (answered by lynnlo)
Prove the identity csc x- cos x cot x = sin... (answered by Fombitz,MathTherapy)
prove that -sin(x)-cos(x)cot(x)=-csc(x) is an... (answered by mananth,Theo)
Verify following is an identity.
(1++sin(x))/sin(x)=(cot^2(x))/(csc(x)-1)
(answered by lwsshak3)
can you please prove this identity
(tan x - cot x) / (tan^2 x - cot^2 x)= sin x cos... (answered by lwsshak3)