Question

Prove that,cot(12°)cot(38°)cot(52°)cot(78°)cot(60°)=cot(60°)

Answer 1

L.H.S
=cot12°×cot78°×cot38°cot52°cot60° {cot12°=tan(90-12°)
=cot12°×tan12°cot38°tan38°cot60° =cot12°=tan 12°}
=1×1×cot60°
=cot60°
Hence proved.

Answer 2

Answer:

=cot(12°)cot(38°)cot(52°)cot(78°)cot(60°)

=cot(90°-78°)cot(90°-52°)cot(52°)cot(78°)cot(60°)

=tan(78°)tan(52°)cot(52°)cot(78°)cot(60°)

=1/cot(78°)×1/cot(52°)×cot(52°)×cot(78°)×cot(60°

=cot(60°)