Question

prove:- tan 82.5 = (under root 3 + under root 2) (under root 2 +1)

Answer 1

Answer:

Step-by-step explanation:

tan 22.5° = √2 - 1 , tan 60° = √3

now

tan 82.5° = tan (60° + 22.5°)

= (tan 60° + tan 22.5° ) ÷ ( 1 - tan 60° tan22.5°)

= (√3+ √2 - 1 ) ÷ { 1 - √3 (√2 - 1)} = {√3+ √2 - 1 } ÷ { 1 - (√6 - √3)}

= {√3+ √2 - 1 }  { 1+√6 - √3} ÷ (- 8 + 6√2)

Answer 2

Answer:

Step-by-step explanation:

tan 22.5° = √2 - 1 , tan 60° = √3

now

tan 82.5° = tan (60° + 22.5°)

= (tan 60° + tan 22.5° ) ÷ ( 1 - tan 60° tan22.5°)

= (√3+ √2 - 1 ) ÷ { 1 - √3 (√2 - 1)} = {√3+ √2 - 1 } ÷ { 1 - (√6 - √3)}

= {√3+ √2 - 1 }  { 1+√6 - √3} ÷ (- 8 + 6√2)