Question

please solve this with steps

Answer 1

Answer:

f tan 25 degree=a then the value of ( (tan 205-tan 115)/(tan 245+ tan 335) in terms of a is?  

If tan 25 degree=a  

then the value of ( (tan 205−tan 115)/(tan 245+ tan 335) in terms of a is  

tan205°=sin205°/cos205°  

=(−sin25°)/(−cso25°)=tan25°=a  

tan 115=tan(90+25) =−cot25° =−1/a  

(tan 245)=sin(180+65°)/cos(180+65°) =(−sin65°)/(−cso65°)=cos25°/sin25° =1/a  

tan 335=sin(360−25°)/cos(360−25°) =(−sin25°)/(cso25°)=−tan25°=−a  

Hence  

( (tan 205−tan 115)/(tan 245+ tan 335) =( (tan 25°−cot25°)/(cot25°−tan25°)  

={a−(−1/a)}/(1/a−a) ={(a²+1)/a)}/{(1−a²)/a} =(a²+1)/(1−a²)

Answer 2

Answer:

OPTION C

Step-by-step explanation:

tan 25° = p

tan 245°

= tan ( 180° + 65° )

= tan 65° [ tan ( A + 180° ) = tan A ]

= tan ( 90° - 25° )

= cot 25° [ tan ( 90 - A ) = cot A ]

= 1/tan 25°

= 1/p ..............( 1 )

tan 335°

= tan ( 180° + 155° )

= tan 155°

= tan ( 180° - 25° )

= tan ( 180° + (-25° ) )

= - tan 25°

= - p ............( 2 )

tan 205°

= tan( 180° + 25° )

= tan 25°

= p .............( 3 )

tan 115°

= tan( 90° + 25° )

= tan ( 90° - ( - 25° ) )

= - cot 25°

= - 1/tan 25°

= - 1/p .................( 4 )

From ( 1 ) , ( 2 ) , ( 3 ) and ( 4 ) we get :

( tan 245 ° + tan 335° ) / ( tan 205° - tan 115° )

⇒ ( 1/p - p ) / ( p - ( -1/p ) )

⇒ ( 1 - p² ) / p / ( p² + 1 ) / p

⇒ ( 1 - p² ) / ( 1 + p² )