= cos3xcosx - sin3xsinx + i(sin3xcosx + cos3xsinx)= cos4x + isin4x 设命题P(n)：zⁿ = (cosx + isinx)ⁿ = cos(nx) + isin(nx)当n = 1时明显成立，P(1)成立 假设当对于某些正整数k，P(k)都成立，i.e. z^k = cos(kx) + isin(kx)当n = k + 1时...
The solution set of equation cos^5 x = 1 + sin^4x is 02:42 The solution set of cos^(5)x=1+sin^(4)x is 01:48 Number of solution of the equation sin((1)/(5)cos^(-1)x)=1 is 04:20 Find the solution set of the equation,3cos^(-1)x=sin^(-1)(sqrt(1-x^(2)... 02...
Show thatf(x)=tan−1(sinx+cosx)is an increasing function on the interval(0,π/4). View Solution Show that the functionf(x)=sin4x+cos4x (i) is decreasing in the interval[0,π4]. (ii) is increasing in the interval[π4,π2]. ...
What is the domain of the function (cos x)/(1 - sin x)? What are the domain and range of the function y = tan(x)? What is the domain and range of y = csc(x)? What is the domain of y = 10 - sqrt(3-x)? What is the domain of h(x) = \sqrt{x^2 - 4x - 5}?
Verify the identity. tan x (1 - cot x) = tan x - 1 Verify the identity. tan (x - /4) = tan x - 1 / tan x + 1 Verify this identity: dfrac{1 + tan x}{ sin x + cos x} = sec x Verify the identity. \cot (\frac{x - \pi}{2})...
The definite integration gives the exact area under the curve by using the function of the curve. Some formulas of the integration are as follows: $$\begin{align} \int \cos x \cdot dx &= \sin x+ c \\[0.2cm] \int \sec^{2} x \cdot dx &= \tan x +c \\[0.2cm] \int \sin...
Question: What is the exact value of {eq}\int_0^4 e^x \,dx {/eq}? Definite Integral: The definite integral of a function {eq}f(x) {/eq} over the interval {eq}[a,b] {/eq} {eq}\displaystyle \int_{a}^{b} f(x) \; dx {/eq} ...
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limlimits _(x→ 0) (sin 3x)(sin 4x)=limlimits _(x→ 0) (3cos 3x)(4cos 4x)= (3⋅ 1)(4⋅ 1)= 34 [We rewrite (sin 3x)(sin 4x) as (sin 3x)(3x)⋅ (4x)(sin 4x)⋅ 34. As x → 0, so do 3x and 4x; the fraction approaches 1⋅ 1⋅ 34.]...
cos4xsin3x−cos2xsinxsin4xsinx+cos6xcosx=tan2x View Solution What is the value ofsin(x+y)−2sinx+sin(x−y)cos(x−y)+cos(x+y)−2cosx×[sin10x−sin8xcos−10x+cos8x]? {[sin(x+y]−2sinx+sin(x−y)}/[cos(x−y)+cos(x+y)−2cosx]}×[(sin10x−sin8x)/...