Sinar cosCota) Cosr cos (p+oar) g- sin ( Cog2or) PrOve Sinar cosCota) Cosr cos (p+oar) g-...
prove the identities g. CSC A-sin A = cos A cot A Solution:
5. Prove the following identity. (sin x + cos x) = 1+sin 2x 6. If cos(x) = , and x E QIV , find the exact value of each of the following. a.sin (2x) b.cos cos()
yl -y Using the fact that (cos x)' = - sin x, prove that | cos x- cos for all , yE R. (Hint: MVT)
Essential_Mathematical_Meth_Arfken_Weber_ 1.3.7 Using the vectors P = ˆx cos θ + ˆy sin θ, Q = ˆx cos ϕ − ˆy sin ϕ, R = ˆx cos ϕ + ˆy sin ϕ, prove the familiar trigonometric identities sin(θ + ϕ) = sin θ cos ϕ + cos θ sin ϕ, cos(θ + ϕ) = cos θ cos ϕ − sin θ sin ϕ.
Is the following equation an identity? If so, prove it. sin- x - cos x cos x = sin’x - cos x The given equation is an identity. sinx - cos*x = (sin’x)2 – (cos?x)2 = (sinºx – cos x) (sinºx + cos²x) = (sin x – cos2x) (1) = sinºx - cos x. The given equation is not an identity. The given equation is an identity. sin- x - cos*x = (sin?x)2 – (cos2x)2 (sinºx – cos x) (sinºx...
13. Evaluate, S sin 5x cos x dx. Also prove that, 52" sin mx cos nx dx = 0 Using reduction formula *****
Prove the identity. 2 sin le coso + cos 40 = 1 - sin e
2.13 Probiems 73 216 Prove de Moivre's formula (cos θ + j sin θ)" = cos(n θ) + j sin(ne). where n is an integer 217 Use de Moivre's formula, given by Eq. (2.80), to develop the rectangular and polar form representations of the (2.80) following complex numbers: 2.18 Show that 219 Determine the roots of the following second-degree polynomials (a) (G)-2s2 -4s + 10, 2.13 Probiems 73 216 Prove de Moivre's formula (cos θ + j sin θ)" =...
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [0, 2T] and φ in [0, π] -3 cos(θ) sin(φ), 5 sin(θ) sin(φ),-15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 3 cos(9) sin(9),-5 sin(θ) sin(9), 15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 v 16 sin2(0) sin2@c 216 cos2@t9(3 cos(θ) sin(φ), 5 sin(θ) sin(φ) , 15 cos(q) 216 cos(φ)...
14. Prove the trigonometric identity: (4) 2) (sin x + cos x)() come an d sin 2x – cas e