Question

prove that cot 35+cot 85+cot 155=0​

Answer 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