Prove that $1 + \frac{cos 105 + cos 165}{sin 105 + sin 375} = 0$ $1+(cos105+cos165)/(sin105+sin375)=0$ ?

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Answer 1 · 2018-05-14T14:21:01

$L H S = 1 + \frac{cos 105 + cos 165}{sin 105 + sin 375}$ $LHS=1+(cos105+cos165)/(sin105+sin375)$

$= 1 + \frac{2 cos 135 cos 30}{2 sin 240 cos 135}$ $=1+(2cos135cos30)/(2sin240cos135)$

$= 1 + \frac{cos 30}{sin (90 \cdot 3 - 30)}$ $=1+(cos30)/(sin(90*3-30))$

$= 1 + \frac{cos 30}{- cos 30}$ $=1+(cos30)/(-cos30)$

$= 1 - 1 = 0 = R H S$ $=1-1=0=RHS$

Prove that 1+cos105+cos165sin105+sin375=01+(cos105+cos165)/(sin105+sin375)=0?