cos38cos46-sin14sin22=1/2cos24
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Answered by
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hello users ......
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 ⭐✡
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 ⭐✡
Answered by
0
Answer:
Step-by-step explanation:
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.....
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