Question

tan 25=a prove that (tan155- tan 115)/(1+tan 155 tan 115)

Answer 1

tan 25 = a

=> tan 155 - tan 115

= tan (180-25) - tan (90+25)

= -tan 25 - (-cot 25)

= -tan 25 - (-1/tan 25)

= -a + 1/a

= -a²+1/a

= (1-a²)/a

=> 1+ tan 155 . tan 115

= 1 + tan (180-25) . tan (90+25)

= 1 + (-tan 25) . (-cot 25)

= 1 +tan 25 . cot 25

= 1 + tan 25 . 1/tan 25

= 1 + a.1/a

= 1 + 1

= 2

So,according to given question,

= (tan155- tan 115)/(1+tan 155 tan 115)

= {(1-a²)/a} / 2

= (1-a²)/2a

formula used :

tan (180-@) = - tan@

tan (90+@) = -cot@

cot @ = 1/tan@

hope it helps

Answer 2

here's ur answer hope this will help you