Prove that :

tan (55° + x) = cot (35° - x)

Given equation : tan (55° + x) = cot (35° - x)

Solving L.H.S.

⇒ tan (55° + x)

⇒ tan [90° - (35° - x)]

By formula,

tan (90° - θ) = cot θ

⇒ cot (35° - x)

Since, L.H.S. = R.H.S.

Hence, proved that tan (55° + x) = cot (35° - x).