Question

Express $\frac{(\sqrt{3} cos 25\textdegree + sin 25\textdegree)}{2}$ as a sine of an angle.

Answer 1

it is given that, (√3 cos25° + sin25°)/2

= [ (√3/2). cos25° + (1/2). sin25° ]

we know, sin60° = √3/2 and cos60° = 1/2

so, [ (√3/2). cos25° + (1/2). sin25° ] = [ sin60°. cos25° + cos60° . sin25° ]

we know, sinA.cosB + cosA.sinB = sin(A + B)

so, [ sin60°. cos25° + cos60° . sin25° ] = sin(60° + 25°)

= sin85°

Answer 2

given:-
(√3 cos25° + sin25°)/2

= [ (√3/2). cos25° + (1/2). sin25° ]

we know;-
sin60° = √3/2 and cos60° = 1/2
sinA.cosB + cosA.sinB = sin(A + B)

so, [ (√3/2). cos25° + (1/2). sin25° ] = [ sin60°. cos25° + cos60° . sin25° ]


so, [ sin60°. cos25° + cos60° . sin25° ] = sin(60° + 25°)

= sin85°