Question

prove that (cos8+sin8)/(cos8-sin8)=tan53​

Answer 1

divide the function by cos8

you'll get -

=> (1+sin8/cos8) / (1-sin8/cos8)

= (1+tan8) / (1-tan8)

we know that tan 45 =1

thus function can be written as (tan 45 + tan 8 )/(1 - tan45 * tan 8)

this is of the form tan(a+b) where a= 45 & b=8

=>(tan 45 + tan 8 )/(1 - tan45 * tan 8) = tan(45+8) = tan 53

tan 53 is RHS

proved