Question

show that tan48 tan23 tan42 tan67=1​

Answer 1

Answer:-

We need to prove that

tan48°tan23°tan42°tan67°=1

Solving LHS

= tan48°.tan42°.tan23°.tan67° =tan48°.cot(90°-42°).tan23°.cot(90°-67°). (As tan∅=cot (90°–∅)

=tan48°.cot48°.tan23°.cot23°

= 1 (as tanA=1/cotA)