QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

Q: Sinxtsina3x COSX+ COS 32 tan 22

A:

Q: 4. To integrate using trigonometric substitution the functio dx -2x we let x = sec 8 - 2

A: Given indefinite integral is ∫dxx2+2x We can solve by using the trigonometric substitution. Given…

Q: Find the value →21. csc (sec- 2) + cos (tan¬1 (– V3))

A:

Q: [sin³ 4x cos 4xdx

A: We can find the answer as below.

Q: sinx = 5/13, x E 5,1], then cosx =?

A: We are solving the problem by the property of trigonometry ratio.

Q: arc sin(3i/4)

A: We know that, Domain of sin-1x is -1≤x≤1.

Q: tan x sec X 3 10 cos xdydx

A: Given : Double integral ∫0π/2∫0tan x sec x y3 cos10x dydx   To find : Evaluate the given double…

Q: Express sin(x +y+z) in terms of cosine and sines of x, y, z.

A: Associative Law: A+B+C=A+B+C=A+B+C Distributive Law: AB+C=AB+AC Left distributive lawA+BC=AC+BC…

Q: and sin x<0, find: Sin (2x) If cosx = 12

A: cos(x) = π/12  Then,  sin(x)  =  1-cos2x  =  1-π2122  =  144-π212

Q: tan(e) cos(0) - sec(0)

A:

Q: Using Euler' formula, show that sin 2x = 2 sin x cosx

A: Euler's Formula used.

Q: Sec (Cosx) dydx 1- Sin

A:

Q: Prove the equation Sin^2xcos^3x=(sin^2x-sin^4x)(cosx)

A:

Q: Find 7 sin² (7x) dx

A:

Q: value of cos x is given. Find sin x and 3T xET, 15 X= 17'

A:

Q: The simplified form of [csc(-x) +cos(-x)] - [10 sin² r sec²z]

A:

Q: cotx (1- cos 2x) = sin 2x

A: Formulae used: 2sinx cosx = sin2x cotx = cosxsinx cos2x = 1-sin2x

Q: lim, 20 sin5x.cot2x = ?

A:

Q: 2. Is trigonometric substitution needed to evaluate /9 - x² dx?

A:

Q: snip

A:

Q: ∫sin5(6x)cos(6x)dx

A: ∫xn=xn+1n+1+C

Q: COs 2x cotx x – tanx %3D sinx · cOsx

A:

Q: tan x + sin x Express in terms of cosine cSC x + cotx only

A: Given expression: tan x+sin xcsc x+cot x

Q: Sine- -Cos zo

A: Using trignometric property

Q: Prove + cosß)* +(sina + sinß) = 4cos² a - B) %3D

A:

Q: tan + cosxtan sinx %3D

A: SOME TRIGONOMETRY FORMULAS: 1.)cos2x= cos2x- sin2x2.) cos(2x)= 2cos2x-13.)cos(2x)=…

Q: tan x dx sec x+4 cosx 5.

A:

Q: 9. tanx + secx = COSX 1- sinx

A: tanx+secx=cosx1-sinxsinxcosx+1cosx=cosx1-sinx1+sinxcosx=cosx1-sinx1+sinxcosx=cosx1-sinx×1+sinx1+sinx…

Q: sin 5tdt V1+ cos /1+cos5t

A: We need to evaluate ∫sin 5t dt1+cos 5t                                    (1) Let  1+cos 5t = u On…

Q: Why is cos(sin^-1(x)) equal to sqrt(1-x^2)?

A:

Q: S(sec; - sin) do

A: We know that integration power rule is  Integration of (xn) = xn+1/n+1.   Here i attached the…

Q: cos xdx 54-sin²x

A:

Q: Express sin 0 cos 0 in terms of a if cot 0 = a

A:

Q: Find a value of x that satisfies the equation sin (-84°) = cos (x). %3D

A: To find: The value of x. Given: The equation sin-84°=cos x. Concept used: sin-θ=-sin θ sin3π2-x=-cos…

Q: [sin³ (2) cos(4) dx

A: Follow the procedure given below.

Q: Integrate cosx cos (x-a)

A:

Q: sin3xdx Cos4x

A:

Q: Solve cos ( tanx) = sin cot! 3 4

A:

Q: Prove (cosa + cosB) + (sina + sinß)° = 4cos²- « - B) %3D

A: Prove this equation by using some trigonometry identity

Q: sin 3x cos“ 3xdx

A:

Q: cos 2x cotx-1 1+sin 2x cotx+1 20

A:

Q: cos 2x sin2x Cotx

A: Solution: The objective is to find the value of the given expression

Q: 8. If sin x- cos x = 3, find sin x sec x

A: given: sinx-cosx=13 to find: sinxsecx

Q: • tan xcos x = cotx %3D cScx • (1- sinx)[1+ sin(-x)] = •csc?x - cot2x =

A: We need to simplify the given trigonometric expressions.

Q: if sinx=1/8 and x is in quadrent 1, then cos(180-x)=???

A: Simplify cos(180-x),

Q: TI tant@-2 tan Bzl show that 2cose - Cos"B2o

A:

Q: sin³ 4z cos° 4zdz

A: Here we have to integrate the given integral.

Q: Find sin 0 and tan 0 if the terminal side of 0 lies along the line y = -7x in QII. sin 0 = tan 0:

A: Given that terminal side of ϑ lies along the line y = -7x. Note that the slope of the line y = -7x…

Q: How do you differentiate y=arctan(cosx)?

A: The function given is

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.