Math, asked by pandupyapili, 5 months ago

prove that cot 35+cot 85+cot 155=0​

Answers

Answered by sharanyalanka7
1

Answer:

0

Step-by-step explanation:

Correct Question :-

cos35° + cos85° + cos155° = 0

Solution :-

Taking L.H.S :-

= cos35° + cos85° + cos155°

We can write,

35° as :- 60°-25°

85° as :- 60° + 25°

= cos(60°-25°) + cos(60°+25°) + cos155°

We know that :-

cos(A+B)+cos(A-B) = 2cosAcosB

= (2cos60°cos25°) + cos155°

= (2\sf\times \dfrac{1}{2} cos25°) + cos155°

= cos25° + cos155°

We know that :-

CosC+cosD = 2  \times  cos\dfrac{ C+D}{2} \times  cos\dfrac {C-D}{2}

 = 2 \times cos \bigg( \dfrac{25 + 155}{2} \bigg) \times cos \bigg( \dfrac{25 - 155}{2}  \bigg)

 = 2 \times cos90 \degree \times cos75 \degree

 = 2 \times 0 \times cos75 \degree

= 0

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