Question

prove that-cos 55 degree + cos 65 degree + cos 175 degree=
0

Answer 1

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Answer 2

To prove:  $\cos 55^\circ+\cos 65^\circ+\cos 175^\circ=0$

We will start from left side

$\Rightarrow \cos 55^\circ+\cos 65^\circ+\cos 175^\circ$

Formula:

$\cos(A\pm B)=\cos A\cos B+\sin A\sin B$

$\Rightarrow \cos (60-5)^\circ+\cos (60+5)^\circ+\cos (180-5)^\circ$

$\Rightarrow \cos60^\circ\cos5^\circ+\sin60^\circ\sin5^\circ+\cos60^\circ\cos5^\circ-\sin60^\circ\sin5^\circ-\cos5^\circ$

$\Rightarrow \cos60^\circ\cos5^\circ+\cos60^\circ\cos5^\circ-\cos5^\circ$

$\Rightarrow 2\cos60^\circ\cos5^\circ-\cos5^\circ$

$\Rightarrow \cos5^\circ-\cos5^\circ$

$\Rightarrow 0=RHS$

0=0, True

Hence Proved