Question

prove without using trigonometric table
sin² 25° + sin² 65° = 1

Answer 1

L.H.S.=>
= sin²25 + sin²65
= sin²25  + sin²(90-25)
= sin²25 + cos²25                  (as sin(90-Ф) = cosФ)
 = 1                                        (as sin²Ф+cos²Ф = 1)
proved

Answer 2

sin^2  25 + ({sin(90-25})^2= sin^2 25+ cos^2 25= 1
   using   sin(90-x= cosx)