Question

prove that sin5x-2sin3x+sin3x/cos5x-cosx=tanx​

Answer 1

Hope this helps you

Answer 2

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sin C − sin D = 2 cos(C+D/2) sin

cos C − cos D = −2 sin(C+D/2) sin (C−D/2)

LHS = sin 5x−2sin3x+sinx / cos5x−cos x

= (sin 5x−sin 3x)−(sin3x−sinx) / cos5x−cosx

= 2cos4xsinx−2cos2x sinx / -2sin3xsin2x

= 2sinx(cos 4x−cos2x) / -2sin3xsin2x

= −2 sin 3x(2sinxcosx) / -2sinx(−2sin 3xsin x)

= sin x / cos x

= tan x = RHS

LHS = RHS