Question

1/2cos24°=cos38°×cos46°-sin14°×sin22°​

Answer 1

$\large{ \textsf{\textbf {\pink {➽ \: \: Solution\: }}}}$

we have to prove that :

cos38cos46-sin14sin22=1/2cos24

solution:-

formula used:

cos a cos b = 1/2 [ cos (a+b) + cos (a-b)]

&

sin a sin b = 1/2 [ cos (a - b) - cos (a + b) ]

&

cos C + cos D = 2 cos {( C+D)/2} cos {(C-D)/2}

Here,

Taking LHS ;

cos38cos46-sin14sin22

= 1/2 [ cos ( 38 +46 ) + cos ( 38 - 46 ) ] - 1/2 [ cos (14 - 22 ) - cos ( 14 + 22) ]

= 1/2 [ cos 84 + cos (- 8) ] - 1/2 [ cos (-8) - cos 36 ]

= 1/2 cos 84 +1/2 cos (-8) - 1/2 cos (-8) + 1/2 cos 36

= 1/2 [ cos 84 + cos 36 ]

= 1/2 [ 2 cos{ ( 84+36)/2} cos {(84 - 36)/2} ]

= 1/2 × 2 × cos (120/2) cos 48 /2

= 1/2 cos 24 ...( cos 60°= 1/2 )

= RHS

Hence;

Proved..

✡⭐ hope it helps ⭐✡

Answer 2

Answer:

$\huge \underline \pink {answer}$

we have to prove that :

cos38cos46-sin14sin22=1/2cos24

solution:-

formula used:

cos a cos b = 1/2 [ cos (a+b) + cos (a-b)]

&

sin a sin b = 1/2 [ cos (a - b) - cos (a + b) ]

&

cos C + cos D = 2 cos {( C+D)/2} cos {(C-D)/2}

Here,

Taking LHS ;

cos38cos46-sin14sin22

= 1/2 [ cos ( 38 +46 ) + cos ( 38 - 46 ) ] - 1/2 [ cos (14 - 22 ) - cos ( 14 + 22) ]

= 1/2 [ cos 84 + cos (- 8) ] - 1/2 [ cos (-8) - cos 36 ]

= 1/2 cos 84 +1/2 cos (-8) - 1/2 cos (-8) + 1/2 cos 36

= 1/2 [ cos 84 + cos 36 ]

= 1/2 [ 2 cos{ ( 84+36)/2} cos {(84 - 36)/2} ]

= 1/2 × 2 × cos (120/2) cos 48 /2

= 1/2 cos 24 ...( cos 60°= 1/2 )

= RHS

Hence;

Proved..