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If cos(A+B)sin(C+D)=cos(A-B)sin(C-D), pr...

If `cos(A+B)sin(C+D)=cos(A-B)sin(C-D)`, prove that `cot A cot B cot C=cotD`.

Text Solution

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`cos(A+B)sin(C+D)=cos(A-B)sin(C-D)`
or `(cos(A+B))/(cos(A-B))=(sin((C-D))/(sin(C+D))`
or `(cos(A+B)+cos(A-B))/(cos(A+B)-cos(A-B))=(sin(C-D)+sin(C+D))/(sin(C-D)-sin(C+D))`
Or `(2cos A cos B)/(-2sin A sinB)=(2sinC cos D)/(-2sin D cosC)`
or `cotA cotB=tanC cot D`
or `cot A cot B cot C=cotD`
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