tan : sin z :: cot : cos r cos/ sin O 1/tan O cos csc csc / sec

Q: Verify (tan x + cot x)(cos x + sin x) = cscx + sec x sin* x – cos“ x = sin? x - cos? x

A: Given that prove tanx+cotxsinx+cosx=cscx+secx   And sin4x-cos4x=sin2x-cos2x

Q: Verify the identity:csc x - cos x cot x = sin x.

A:

Q: Evaluate: cos [sin cos[tan' +4 sin sec (" )

A:

Q: Assume that sin 0 = , where n/2 < 0 < n. Find: (a) tan 0 (b) sin 20 (c) csc

A:

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

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

Q: Find sin x if cot x = -(√3)/2 and cos x

A:

Q: Verify the identity. tan(0) sin(0) + cos(0) = sec(0) tan(0) sin(0) + cos(0) sin(0) + cos(0) cos(0)…

A: (1)tan(θ)sin(θ)+cos(θ)=sec(θ)tan(θ)sin(θ)+cos(θ)=sin(θ)cos(θ)·sin(θ)+cos(θ)…

Q: tan (0) +1 1) sec(e) = sec(0) cos(@) +1 2) tan (0) cos(@) sec(@)-1

A: See the details solution in below

Q: verify the identity: sin(x+y) + sin(x-y)         = tanx cos(x+y)+cos(x-y)

A:

Q: 2. cot 0= sin 0 = cos 0 = tan 8 = csc = sec 0 = 2

A:

Q: sin: tan cos : cot: cos csc O csc / sec 1/tan cos / sin

A: Solution:

Q: Prove the identity tan+cot 0 = csc sin + sec 0 + cos e

A:

Q: tan x - cot x Cos 2x Cot X t tanX

A: Given: tanx-cotxcotx+tanx=-cos2x

Q: tan e = 4 and 0 terminates in QIII 3 sin 0 Cos e = Csc e sec e cot 0

A:

Q: verify the trigonometric identity: cot x( sec x-cos x)= sinx

A:

Q: Establish the identity. (sec 0+ tan 0)( sec 0- tan 0) = 1

A: We have to prove

Q: tan( sin " + cos") - %3D

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Let tan (0) = 3 with 0 in QI. Find sec (20). 10 sec (20) =

A:

Q: snip

A:

Q: Establish the identity. sec 0 3 sin 0 = 4 tan 0 csc 0 cs 0

A: To prove that secθcosecθ+3sinθcosθ=4tanθ

Q: 5. Establish the identity: tan 0 +cot 0 = sec 0 csc LHS COSE Sine Sude

A: consider the given identities

Q: Prove: sec 0 + tan(-0) cot 0 - cos (0) = sec 0 tan 0

A:

Q: cos O sec 0 48. cos? wwww. www + tan? 0

A: We have to simply the given expression.

Q: Evaluate S tan'x sec'x dx sec x 2 secx sin x - 2 sin'x + sin'x +C 3 3 Option 1 O Option 2 - cos'x +…

A:

Q: Show that (sec x) = sec x tan x. dx Note: You may assume it is known that (sin x) = cos x and :(cos…

A:

Q: csc x sec x = sec x + cscx cot x %3D

A: By taking left hand side and using trigonometric formula we prove left hand side equals to right…

Q: HW/Prove that: . (1) tanx=cot! tan"x= cot-1 (2) sin x = csc -11. (3) sin (sin x) = x

A: We have to prove the identities 1. tan-1x=cot-11x2. sin-1x=csc-11x3. sin-1sinx=x

Q: 16. (tan 0+cot@y = sec 0+ csc? 0 tant

A:

Q: Assume that sin 0 , where n/2 < 0 < 1. Find: (a) tan 0 (b) sin 20 (c) csc

A:

Q: 1 sec @ — tanө %3D sece + tan0

A: rationalizing LHS and using trigonometry formula's to get RHS

Q: Show that (sec x) = sec x tan x. Note: You may assume it is known that (sin x) = cos x and :(cos x)…

A:

Q: sec : tan/ sin :: cos :

A: As we know cos and sec are reciprocal of each other.  Therefore sec:tan/sin Then cos:sin/tan

Q: FTi csc x = 4,90° < x < 180°, then %3D sin cos %3D tan %3D II II

A:

Q: sec : tan/ sin : cos : cos csc cot/csc O cos/sin 01/ tan

A: Here we have find      sec : tan/sin :: cos : ______ .

Q: OIf tan o =} OcOc Ź, find sin s. Sin %3D

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 1. cos t (1 + tan²t) sin ß sec ß + cos ß csc ß 2.

A: Given : 1. cost1+tan2t2. sinβsecβ+cosβcscβ

Q: Simplify: csc^2 θ - cot^2 θ + 2 - (sin^2 θ +cos^2 θ) + sec^2 θ - tan^2 θ  = ?

A:

Q: Prove tan x + cos x = sin x (sec x + cot x).

A: We have to prove the identity: tan x+cos x=sin x sec x+cot x We know the relation between…

Q: Verify the identity: csc x - cos x cot x = sin x.

A: Given identity, cscx-cosxcotx=sinx

Q: Find cot(x) and cos(x) if sin(x) =1/4 and tan(x) >0

A:

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: Verify the identity. sec(x) + csc(x) tan(x) + cot(x) cos(x) + sin(x)

A:

Q: Find sec 0 if tan 6 and 0 terminates in QIII. sec e = :- 4 sec e = 3 5 sec 0 = %3D sec 6 sec 0: %3D…

A:

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

A:

Q: Establish the identity. sec 0• sin 0 = tan 0

A:

Q: If y = Cot-1 - tan-1x, X then y'

A:

Q: Verify identity cot x sec x sin x = 1.

A: Verify: cotxsecxsinx=1

Q: tan x- cotx + 2 cos? x = 1 tan x + cotx

A: tanθ =sinθcosθ cotθ=cosθsinθ sin2θ+cos2θ=1