Question

iii) Prove that Tan 72° = Tan 18° + 2 Tan 54 degrees​

Answer 1

Step-by-step explanation:

we have to prove that tan72 ° = tan18 ° + 2tan54 ° [ you did mistake in typing ] we know , tan ( A - B ) = ( tanA - tanB ) / ( 1 + tanA . tanB ) tan54 ° = tan ( 72 ° - 18 ° ) or , tan54 ° = ( tan 72 ° - tan18 ° ) / ( 1 + tan72 ° . tan189 ) or , tan54 ° ( 1 + tan72 ° . tan18 ° ) = tan72 - tan18 ° we know , tan72 ° = tan ( 90 ° - 18 ° ) = cot18 ° or , tan54 ° ( 1 + cot18 ° . tan18 ° ) = tan 72 ° - tan18 ° or , tan54 ° ( 1 + 1 ) = tan 72 ° - tan18 ° or , 2tan54 ° = tan 72 ° - tan18 ° hence , tan72 ° = tan18 ° + 2tan54 LHS = RHS