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Question

Mathematics Question on Trigonometric Functions of Sum and Difference of Two Angles

Prove that cotx cot2x-cot2x cot3x-cot3x cotx=1.

Answer

L.H.S. = cotx cot2x-cot2x cot3x-cot3x cotx

= cotx cot2x-cot3x (cot2x+cotx)

= cotx cot2x-cot(2x+x) (cot2x+cot x)

=cotxct2x−[cot2xcotx−1cotx+cot2x](cot2x+cotx)=cotxct2x-[\frac{cot2xcotx-1}{cotx+cot2x}](cot2x+cotx)

[cot(A+B)=cotAcotB−1cotA+cotB][cot(A+B)=\frac{cot AcotB-1}{cotA+cotB}]

= cotx cot2x-(cot 2x cotx-1)

= 1 = R.H.S.