Cosx -1-2- x - IIIrd quadrant

cosx>=( 1/2) as>xin>3^rdquadrant> ∴>x=π+(π/3) =(4π/3) ...

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Complex Numbers

cosx =-1/2; x...

Question

$c o s x = \frac{- 1}{2}; x \in I I I^{r d}$ quadrant

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Prove that:

(i) If $c o s x = - \frac{3}{5}$ and x lies in the IIIrd quadrant, find the values of $c o s \frac{x}{2}, s i n \frac{x}{2}$ and sin 2x.

(ii) If $c o s x = - \frac{3}{5}$ and x lies in the IInd quadrant, find the values of sin 2x and sin $\frac{x}{2}$

\cos x = - \frac{3}{5}

\cos \frac{x}{2}, \sin \frac{x}{2}, \sin 2 x

\cos x = - \frac{3}{5}

\sin \frac{x}{2}

cos x = - \frac{1}{\sqrt{2}}

x \in 3 r d

sin \frac{x}{2}, cos \frac{x}{2} a n d tan \frac{x}{2}

tan x = - \frac{4}{3},

I I

cos x = - \frac{1}{3}

I I I

sin \frac{x}{2}, cos \frac{x}{2}

tan \frac{x}{2}

cos x = - \frac{1}{3}, x

I I I .

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