1-sin' x 3D sin.x 6. cosxcotx

Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

A:

Q: 4 cos 4 cos dx () х3 sin3 4 - у4 - х dx

A: (1) using integration by substitution∫4 cos1x2x3 sin31x2 dxlet   sin1x2=udifferentiate both…

Q: (g) tan sec2 dx (c) sin“(3x) cos (3x) dx CoS'

A: Given: I1=∫sin43xcos33xdx, I2=∫tan4x2sec2x2dx

Q: |5sin(4x + 5) sin(2x --) dx

A: We need to evaluate the given integral. We will use the formula  Cos(A+B)-Cos(A-B)=-2 SinA SinB

Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: cos 2x +1 sin 2x Prove that Please show proper steps sin 2x 1- cos 2x

A:

Q: 6. cos x(csc x secx) secx) cotx

A:

Q: If y=sin 2x sin 3x sin 4x then find y''

A:

Q: 5) 3tan-1x + sin-x = 4

A:

Q: Prove sin 2x cot x (1 - cos 2x)

A:

Q: 2-sec2x: COS2X = COS X

A: Given query is to verify the identity

Q: If y=sin(sinx) show that y''+(tan x) y'cos2x=0

A:

Q: Prove: sin (2 cosx) = 2x1-x

A:

Q: 5. y = sin² (In .x)

A:

Q: 16. Using the Quotient tanx= sinx/cosx to prove d/dx tanx=sec2x

A: Quotient rule of differentiation

Q: -sin^2(x)=cos(2x) from [-pi, pi]

A:

Q: sin(2x) cos(2x) dx 1+ cos(4x)

A: The complex form of integral can be converted to simple integral using integration by substitution…

Q: 21. cos x cos 2x + sin x sin 2x

A:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: 1 Differentiate f(æ) = sin-(4x). Use exact values. = (x),f

A: We use the chain rule for differentiation

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

A: Topic = Trigonometry

Q: Find the exact value of sin(x - y) if sin x = 3 ≤ y ≤ 2. on ≤x≤ and sin y=-3 on

A:

Q: Find sin(2x), cos(2x), and tan(2x) from the given tan(x) = -, cos(x) > 0 %3D sin(2x) = %3D cos(2x) =…

A: Given: tanx=-16,   cosx>0 sin2x can be calculated as, sin2x=2tanx1+tan2x          =2×-161+-162…

Q: Prove sin (90◦+x) + sin (90◦−x) = 2 cosx

A:

Q: 1-Sinx finel y 14 Sinx

A: Consider the given function, y=1-sinx1+sinx use the quotient rule of the differentiation which…

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

A:

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

A:

Q: If y = sin 2x sin 3x sin 4x then find y".

A:

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: Prove 2tan x cos (3x) = sec x (sin(4x) - sin (2x))

A: Topic- trigonometry

Q: 15. integral sin 4x cos 4xdx

A:

Q: If ln sin x = 1 + ln cos x, then x is equal to what.

A: Given that , lnsinx=1+lncosx find value of x.

Q: 7. Show that sin (+ x) = -cosx.

A:

Q: 2 , 1 + sinx +. D. cosx cosx il + sin.x

A:

Q: 1+ cos x sin x 7. Verify: ¹ 11 csc x + cotx

A:

Q: 4 If cos x = csc x < 0, then sin 2x = cos 2x = tan 2x = ||

A:

Q: cos^2x+sin^2x/cos^2x=

A:

Q: 3) (sinx + cos x)² = sin 2x + 1 COS %3D

A: We have to prove that  (Sinx+cosx)^2=sin(2x)+1

Q: Find sin 2x, cos 2x, and tan 2x if tanx 2 and x terminates in quadrant I. sin 2x cos 2.x !! tan 2.x

A: Given, tan x = 2 x terminates in quadrant in I We have to find the value of sin2x, cos2x and tan2x

Q: Show that sin²(x) cos(x) = sec(x) – cos(x)

A: We need to show the following. So,         Manipulating right side=secx-cosx=1-cos2xcosx=sin2xcosx

Q: 3. у %3D tan1(sinh 2x) Зсosh-1 (csc) 4. у %3 CSC

A:

Q: 2. / sin² cos² xdx

A: As per our guideline we are supposed to answer only one question you can repost other in next…

Q: . Evaluate cos 3x sin² 3x dx

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: Verify that (sin(x) – cos(x)) = 1- sin(2x)

A: sinx-cosx2=sin2x-2sinxcosx+cos2x     ∵a-b2=a2-2ab+b2=sin2x+cos2x-2sinxcosx=1-sin2x…

Q: Verify the identity. sin 3x 1 = 2 cos x- %3D sec x 2 - sin 2x

A: Given: Verify the identity sin3xsin2x=2cosx-12secx for verifying given identity we solve left hand…

Q: If sinx = siny = a and cosx = cosy = b,then cos(x-y) is

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.