Question

convert the following products into sum or difference. if angles are given in degree evaluate from table 2sin48° cos12°​

Answer 1

we have to convert 2sin48° cos12° into sum or difference and also evaluate the expression using table.

solution : we know, 2sinA cosB = sin(A + B) + sin(A - B)

also 2cosA sinB = sin(A + B) - sin(A - B)

using it we can converts 2sin48° cos12° into sum or difference.

i.e., 2sin48° cos12° = sin(48° + 12°) + sin(48° - 12°)

= sin60° - sin36° [ sum ]

or, 2cos12° sin48° = sin(12° + 48°) - sin(12° - 48°)

= sin60° - sin(-36°) [ difference ]

now we have to evaluate 2sin48° cos12°

2sin48° cos12° = sin60° + sin36°

from table , sin60° = √3/2 = 0.866

and sin36° = √{10 - 2√5}/4 = 0.587

so, = 0.866 + 0.587 = 1.453

Therefore the value of 2 sin48° cos12° = 1.453