2016年3月20日 · Apply the 2 trig identity: sin 2a = 2sin a.cos a sin 8x = 2sin 4x.cos 4x Since sin 4x = 2sin 2x.cos 2x, therefor, sin 8x = 2(2sin 2x.cos 2x)cos 4x = Since sin 2x ...

2018年4月14日 · f'(x)=8cos(8x) This will require a single application of the Chain Rule, as a result of the 8x. f'(x)=cos(8x)*d/dx8x f'(x)=8cos(8x)

2018年4月14日 · sin^8x=1/128[35-56cos2x+28cos4x-8cos6x+cos8x] rarrsin^8x =[(2sin^2x)/2]^4 =1/16[{1-cos2x}^2]^2 =1/16[1-2cos2x+cos^2(2x)]^2 =1/16[(1-2cos2x)^2+2*(1 …

2018年2月11日 · #lim_(x→0) (sin8x)/x=lim_(x→0) (8sin8x)/(8x)=8lim_(x→0)(sin8x)/(8x)# We now use the well known limit #lim_(vartheta→0) sinvartheta/vartheta=1#

2015年4月26日 · Think about double angle formulas until you think of one that might be useful. sin 2 theta = 2 sin theta cos theta That looks helpful. 2 sin theta cos theta = sin 2 theta so sin …

2015年9月23日 · Let's ignore the integral symbols for now. #=> sin(5x)sin(8x)# It'd be great if we had an identity for this. Maybe w

2016年3月7日 · cos(x)sin(x) = sin(2x)/2 So we have cos(x)sin(x) If we multiply it by two we have 2cos(x)sin(x) Which we can say it's a sum cos(x)sin(x)+sin(x)cos(x) Which is the double angle …

The derivative of \\sin(x) can be found from first principles. Doing this requires using the angle sum formula for sin, as well as trigonometric limits.

2018年5月30日 · f(x) = (sin 5x - sin 3x)(sin 5x + sin 3x) . Use trig identities: #sin a - sin b = 2cos ((a + b)/2)sin ((a - b)/2)#

2018年1月27日 · Following Eshan S's answer we provevthe general trigonometric identity with the double angle formula for sines: