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Prove that cos10°+cos110°+cos130°=0

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Prove that cos10°+cos110°+cos130°=0

Posted by Aparna Sinha 5 years, 8 months ago

CBSE > Class 11 > Mathematics

3 answers

Iram Hasan Hasan 5 years, 8 months ago

Use the formula cosC+cosD:2cos(C+D/2)cos(C-D/2) Use this in the question: 2cos(10+110/2)cos(10-110/2)+cos130=0 2cos60°cos(-50°)+cos130°=0 2×1/2.cos50+cos130=0 cos50+cos130=0 2cos(50+130/2)cos(50-130/2)=0 2cos90.cos40=0 2×0.cos40=0 0=0 H.P

Aparna Sinha 5 years, 8 months ago

Thku

Sia ? 5 years, 8 months ago

<div class="ans_text">

cos 10 + cos 110 + cos 130 = (cos 10 + cos 110) + cos 130
= $2cos \frac{(110+10)}{2}\times cos\frac{(110-10)}{2}$ + cos 130 {using cos C + cos D}
= $2cos \frac {(C+D)}{2}$ $\times$ $cos\frac {(C-D)}{2}$
= $2cos\frac{120}{2}$ $\times$ $cos\frac {100}{2}$ + cos (180 - 50) (As 130 = 180 - 50)
= 2 cos 60 $\times$ cos 50 - cos 50 (Using cos (180 - A) = - cos A)
= 2 $\times$ $\frac{1}{2}$ $\times$ cos 50 - cos 50 ( As cos 60 = $\frac{1}{2}$ )
= cos 50^o - cos 50^o= 0

</div>

ANSWER

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