Question-83229

Question Number 83229 by peter frank last updated on 28/Feb/20

Commented by jagoll last updated on 28/Feb/20

(iii) \frac{\cos 3 A - \cos 9 A + \cos A - \cos 3 A}{\sin 9 A - \sin 3 A + \sin 3 A - \sin A}

= \frac{\cos A - \cos 9 A}{\sin 9 A - \sin A} = \frac{2 \sin 5 Asin 4 A}{2 \cos 5 Asin 4 A}

= \tan 5 A

Commented by peter frank last updated on 28/Feb/20

t h a n k y o u s i r .

i s i t p o s s i b l e t o f i n d

g e n e r a l v a l u e i n b (i) ?

Commented by jagoll last updated on 28/Feb/20

(i) \cos px + \cos qx = 0

2 \cos (\frac{p + q}{2}) x \cos (\frac{p - q}{2}) x = 0

\Rightarrow \cos (\frac{p + q}{2}) x = \cos \frac{π}{2}

(\frac{p + q}{2}) x = \pm \frac{π}{2} + 2 k π \Rightarrow x = \frac{\pm π + 4 k π}{p + q}

\Rightarrow similarly \cos (\frac{p - q}{2}) x = \pm \frac{π}{2} + 2 k π

x = \frac{\pm π + 4 k π}{p - q}

Commented by peter frank last updated on 28/Feb/20

t h a n k y o u