5) Prove that tan(x) + cot(x) = [sec(x)][csc(x)]

Q: 2: Prove that a) cosx tan3x = sinx tan’x b) (sin x + cos x)² = 1 + sin 2x

A:

Q: 11. Prove the identity sin x 1+ cos x 2 csc x 1+ cos x sin x

A:

Q: 04) Prove that 1- Cos + x) = sin x, 2- (sin x +cos x) sec x = sec2 x %3D

A: We have to prove that following trigonometric identity.

Q: Prove the identity sec x - cos x = sinxtanx

A: To prove the identity

Q: 14. Prove that (1- cos x) csc x = 1

A:

Q: Prove the identity (sin x - cos x)2 = 1 - sin 2x

A:

Q: Prove the identity. cosx 1- sin x 1 = tan x cos x

A: We need to prove the following identity cosx1-sinx - 1cosx = tanx

Q: Prove the identity. cos(3x) − cos^3 x = − cos x sin^2 x − sin x sin(2x)

A:

Q: Prove the identity 1/Cos X - 1/Sec X = Tan X * Sin X

A:

Q: tan(8x) x-0 sin(5x) is indeterminate of type Therefore lim We must use l'Hospital's Rule. The…

A: We are given to find the limit of limx→0 tan(8x)sin(5x); and we have to make use of L hospital rule…

Q: * Prove: sin x = cos COS 2- 2cos x

A:

Q: Prove the identity. sin(2x) 1+ cos(2x) tan(x) = 2 sin(x) · sin(2x) 1+ cos(2x) 1+ (2 cos?(x) – 1) 2…

A:

Q: 1) Prove that sin 0 tan 0 + cos 0 = sec 0.

A:

Q: Prove that cos 2x | tan x + cos 2x ).

A: we need to prove, 1-Cos2x1+Cos2x = tanx

Q: 1 Verify the identity 1 = 2 tan x sec x %3D 1-sin x 1+sin x

A:

Q: 7) Verify the identity (cot x – csc x)(cos x + 1) = -sin x

A:

Q: Prove the identity. sin'x cos'x= (cos'x- cos"x) sin x

A:

Q: Prove the identity: (sin x – cos x)(sin x + cos x) = 2 sin² x – 1

A: As value of cosθ and sinθ revolves around +1 to -1 , they take different values depending on the…

Q: 1 1 Prove -2 secx tan x 1+ sin x 1- sin x

A:

Q: Verify the identity: (tan x + tan y)/(1 - tan x tan y)= (sin x cos y + cos x sin y)/ (cos x cos y -…

A: Given: verify that tanx+tany1-tanxtany=sinxcosy+cosxsinycosxcosy-sinxsiny for verifying given…

Q: Prove the identity  Cos x/1+sin x + Cos x/ 1-sinx = 2sec x

A:

Q: 24. Prove the identity sec(x) (sin(x) + cos(x)) sec(x) + 2 sin(x)

A:

Q: Use the same-derivative argument to prove the identities a. tan-1 x + cot-1 x = pai/ 2   b. sec-1 x…

A: Recall that the mean value theorem is as follows:Suppose f(x) is a function that satisfies both of…

Q: 6. Verify the identity: sin x 1 + cosx 1 + cosx sin x 2 cscx %3D

A: Topic = Trigonometry

Q: 1 Prove that sin x tan x = cos x. cosx

A:

Q: Verify the identity: sec x - 1 = sec x 1- cos x

A: Now , we will verify the identity.  We know,  1/cosx = secx .

Q: 9. Prove. cos x sin x 1 - csc x %3D sec x

A:

Q: Q4: Prove that: secx • cscx = tan x + cot x

A: According to guidelines we should have been able to solve only one question at a time #4

Q: Prove that X X sin 8 2 sin sin x 8 2,

A: The objective of the problem is to prove the equation. sin2π8+x2-sin2π8-x2=12sinx

Q: In(|tan(x) sin(x)|) = 2 In(|sin(x)]) + In(|sec(x)])

A:

Q: 3. Prove the identity tan * COS v t CSC x Sinx=2sinx

A: Prove the identity

Q: Verify the identity: [sin 2x + (sin 3x + sin x)]/[cos 2x + (cos 3x + cos x)] = tan 2x

A: Consider the identity, sin2x+sin3x+sinxcos2x+cos3x+cosx=tan2x To apply the trigonometric identity,…

Q: find maclurin formula in the fourth degree for f(x)=tanx

A:

Q: Prove cos* x – sin* x =1–2sin² x

A:

Q: prove that cos^2 x/2= tanx+sinx/ 2tan x

A:

Q: 3) Prove that b) tan- (*)} = sechx

A: Evaluate the derivative of the given function as follows. ddxtan-1ex=11+ex2ddxex…

Q: 4. Prove that tan x – cos x = sec x – cosʻ x - x- cos cos x – 1. :

A:

Q: Prove the identity. cos x- secx=-sinx tan x 2.

A:

Q: Prove the identity. sec (-x) – sin (–x) tan (–x) = cos cosx

A:

Q: Verify the identity. sin 5x + sin 3x 2 cos x 4 sin x cos3 x - X – 4 sin x cos x 3.

A:

Q: 9. Prove: csc(x)-csc(x)cos² (x) = sin(x)

A: To prove: csc(x)-csc(x)cos2(x)=sin(x) Note that, sin2(x)+cos2(x)=1

Q: 3. Given f(x) = cot(x) sin(x) and g(x) = cos³(-x)(sec² (x)-1) sin² (x) a. Prove that f(x) = g(x).…

A: Given that,  fx=cotxsinx and gx=cos3-xsec2x-1sin2x

Q: Prove that _ d tanx = Sec'x.

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.