if A=22.5 than (1+cosA)(1+cos3A)(1+cos5A)(1+cos7A)=?
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Answered by
15
Refer to the file I've attached . If doubts , then enquire.
hope this assists.
hope this assists.
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parisakura98pari:
do u have any query in this question?
No. Amazing way. Didn't occur to me to do it by substituting the angles directly. THANKS
well thanks for marking it as brainliest...
Answered by
9
(1+cos A)(1+cos 7A) = 1+ cos A + cos 7A + cos A cos 7A
= 1+ 2 cos 4A cos 3A + 1/2 * (cos 8A + cos 6A)
= 1 + 0 + 1/2 (-1 -1/sqrt2)
as 4A= pi/2, 8A= pi, 6A=3pi/4
.
Similarly
(1+cos 3A) (1+ cos 5A)
= 1 + cos 3A + cos 5A + cos 3A cos 5A
= 1 + 2 cos A cos 4A + 1/2 (cos 2A + cos 8A)
= 1 + 0 + 1/2 (1/sqrt2 - 1)
.
Multiply the factors to get
(1/2)^2 - (1/2sqrt2)^2
= 1/4 - 1/8 = 1/8
= 1+ 2 cos 4A cos 3A + 1/2 * (cos 8A + cos 6A)
= 1 + 0 + 1/2 (-1 -1/sqrt2)
as 4A= pi/2, 8A= pi, 6A=3pi/4
.
Similarly
(1+cos 3A) (1+ cos 5A)
= 1 + cos 3A + cos 5A + cos 3A cos 5A
= 1 + 2 cos A cos 4A + 1/2 (cos 2A + cos 8A)
= 1 + 0 + 1/2 (1/sqrt2 - 1)
.
Multiply the factors to get
(1/2)^2 - (1/2sqrt2)^2
= 1/4 - 1/8 = 1/8
Click on the red heart thanks above
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