Question

without using trignometric table, prove that:
(i)sin 53 . cos 37 + cos 53 sin 37 =1
(ii)cos 54.cos 36-sin 54 .sin 36 =0
(iii)sec 70. sin 20 + cos20 .cosec 70 =2
(iv)(sin+ cos 18)(sin 72 + cos 18)=0

Answer 1

sin53xcos37+cos53xsin37=1

LHS

sin(90-37)xcos37+cos(90-37)xsin37

cos37xcos37+sin37xsin37 [by formula]

cos²37+sin²37[by the formula ]

1

hence, LHS=RHS