Question

sin51°+sin156°/cos39°+cos66°​

Answer 1

We know that ,

i ) Two angles are said to be complementary

if their sum is equals 90 degrees.

a ) sin ( 90 - A ) = cos A

b ) cos ( 90 - A ) = sin A

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According to the given problem ,

LHS = sin 51 + cos 81

= sin 51 + cos ( 90 - 9 )

= sin 51 + sin 9

= 2 × sin ( 51 + 9 ) /2 × cos ( 51 - 9 ) /2

[ since trigonometric transformations ,

Sin C + Sin D = 2 Sin ( C + D ) /2 Cos ( C - D ) /2 ]

= 2 sin 60 /2 × cos 42 / 2

= 2 × sin 30 × cos 21

= 2 × (1 / 2) × cos 21 [ since sin 30 = 1 / 2 ]

= cos 21

= RHS

Therefore,

Sin 51 + cos 81 = cos 21

I hope it helps you.