Question

prove that

Cos 9x - Cos 5x/ sin 17x - Sin3x=

- Sin2x/ cos 10x

Answer 1

Answer:

Hey!!

Step-by-step explanation:

LHS = (cos9x - cos5x) / (sin17x-sin3x)

Use the formula,

cosC - cosD = 2sin(C + D) / 2.sin (D-C) /2

sinC - sinD = 2cos (C+D) / 2.sin (C-D) /2

= {2sin (9x+5x) / 2.sin (5x - 9x) / 2} / {2cos(17x+3x) / 2.sin (17x-3x)/2}

=-(sin7x.sin2x) / (cos10x.sin7x)

= - sin2x / cos10x = RHS

 

Thank you...

Answer 2

ĀNSWĒR ⏬⏬

$\frac{cos9x - cos5x}{sin17x - sin3x} = \frac{ - sin2x}{cos10x} \\ \\ by \: using \: \\ \frac{ \cos \: c - cos \: d}{sinc - sind} = \frac{ - 2sin \frac{c + d}{2} sin \frac{c - d}{2} }{2cos \frac{c + d}{2} \: sin \: \frac{c + d}{2} } \\ \\ = \frac{ - 2sin \frac{(9x + 5x)}{2} sin \frac{(9x - 5x)}{2} }{2cos \frac{(17x + 3x)}{2} sin \frac{(17x - 3x)}{2} } \\ \\ = \frac{ - 2sin \: \frac{(14x)}{(2)} sin\frac{(4x)}{(2)} }{2cos \frac{(20x)}{2} sin \frac{(14x)}{(2)} } \\ \\ = \frac{ - 2sin7x \: sin \: 2x}{2cos \: 10x \: sin \: 7x} \\ \\ = \frac{ - sin2x}{cos10x} \: \: l.h.s$

THANKS ✌☺

#HarYanvi ThinkeR ♠ ( Nishu )♥