Question

(iv)
(v) cos 10° + cos 110° + cos 130º = 0​

Answer 1

Answer:

LHS cos10+cos110+cos130

=2cos60cos50+cos130[cosC+cosD=2cos

2

C+D

cos

2

C−D

]

=2×

2

1

cos50+cos130

=cos50+cos130

=2cos90cos40

=2(0)cos40

=0

Answer 2

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cos 10 + cos 110 + cos 130 = (cos 10 + cos 110) + cos 130

⇒2 cos (110 + 10)/2 * cos (110 - 10)/2 + cos 130 ------- {using cos C + cos D = 2 cos (C + D)/2 * cos (C - D)/2 }

⇒ 2 cos 120/2 * cos 100/2 + cos (180 - 50) -------- ( As 130 = 180 - 50)

⇒2 cos 60 * cos 50 - cos 50 -------- (Using cos (180 - A) = - cos A)

⇒2 * 1/2 * cos 50 - cos 50 --------- ( As cos 60 = 1/2)

⇒cos 50 - cos 50

⇒0