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First on any other media jee dates revealed and confirmed So share this channel to recieve more such educational update

NRTI KE APPLICATION FORM ME bache hue do attempt of jee ki dates di hui hai so rest two papers are confirmed and will be held on July and other attempt in August💥💥💥💥💥

📚Notes on Trigonometric Equations and Identities📚 A function f(x) is said to be periodic if there exists some T > 0 such that f(x+T) = f(x) for all x in the domain of f(x). In case, the T in the definition of period of f(x) is the smallest positive real number then this ‘T’ is called the period of f(x). Periods of various trigonometric functions are listed below: 1) sin x has period 2π 2) cos x has period 2π 3) tan x has period π 4) sin(ax+b), cos (ax+b), sec(ax+b), cosec (ax+b) all are of period 2π/a 5) tan (ax+b) and cot (ax+b) have π/a as their period 6) |sin (ax+b)|, |cos (ax+b)|, |sec(ax+b)|, |cosec (ax+b)| all are of period π/a 7) |tan (ax+b)| and |cot (ax+b)| have π/2a as their period ➖Sum and Difference Formulae of Trigonometric Ratios 1) sin(a + ß) = sin(a)cos(ß) + cos(a)sin(ß) 2) sin(a – ß) = sin(a)cos(ß) – cos(a)sin(ß) 3) cos(a + ß) = cos(a)cos(ß) – sin(a)sin(ß) 4) cos(a – ß) = cos(a)cos(ß) + sin(a)sin(ß) 5) tan(a + ß) = [tan(a) + tan (ß)]/ [1 - tan(a)tan (ß)] 6)tan(a - ß) = [tan(a) - tan (ß)]/ [1 + tan (a) tan (ß)] 7) tan (π/4 + θ) = (1 + tan θ)/(1 - tan θ) 8) tan (π/4 - θ) = (1 - tan θ)/(1 + tan θ) 9) cot (a + ß) = [cot(a) . cot (ß) - 1]/ [cot (a) +cot (ß)] 10) cot (a - ß) = [cot(a) . cot (ß) + 1]/ [cot (ß) - cot (a)] ➖Double or Triple -Angle Identities 1) sin 2x = 2sin x cos x 2) cos2x = cos2x – sin2x = 1 – 2sin2x = 2cos2x – 1 3) tan 2x = 2 tan x / (1-tan 2x) 4) sin 3x = 3 sin x – 4 sin3x 5) cos3x = 4 cos3x – 3 cosx 6) tan 3x = (3 tan x - tan3x) / (1- 3tan 2x) ➖For angles A, B and C, we have 1) sin (A + B +C) = sinAcosBcosC + cosAsinBcosC + cosAcosBsinC - sinAsinBsinC 2) cos (A + B +C) = cosAcosBcosC- cosAsinBsinC - sinAcosBsinC - sinAsinBcosC 3) tan (A + B +C) = [tan A + tan B + tan C –tan A tan B tan C]/ [1- tan Atan B - tan B tan C –tan A tan C 4) cot (A + B +C) = [cot A cot B cot C – cotA - cot B - cot C]/ [cot A cot B + cot Bcot C + cot A cotC–1] ➖List of some other trigonometric formulas: 1) 2sinAcosB = sin(A + B) + sin (A - B) 2) 2cosAsinB = sin(A + B) - sin (A - B) 3) 2cosAcosB = cos(A + B) + cos(A - B) 4) 2sinAsinB = cos(A - B) - cos (A + B) 5) sin A + sin B = 2 sin [(A+B)/2] cos [(A-B)/2] 6) sin A - sin B = 2 sin [(A-B)/2] cos [(A+B)/2] 7) cosA + cos B = 2 cos [(A+B)/2] cos [(A-B)/2] 8) cosA - cos B = 2 sin [(A+B)/2] sin [(B-A)/2] 9) tanA ± tanB = sin (A ± B)/ cos A cos B 10)cot A ± cot B = sin (B ± A)/ sin A sin B ➖Method of solving a trigonometric equation: 1) If possible, reduce the equation in terms of any one variable, preferably x. Then solve the equation as you used to in case of a single variable. 2) Try to derive the linear/algebraic simultaneous equations from the given trigonometric equations and solve them as algebraic simultaneous equations. 3) At times, you might be required to make certain substitutions. It would be beneficial when the system has only two trigonometric functions. ➖Some results which are useful for solving trigonometric equations: 1) sin θ = sina and cosθ = cosa ⇒ θ = 2nπ + a 2) sin θ = 0 ⇒ θ = nπ 3) cosθ = 0 ⇒ θ = (2n + 1)π/2 4) tan θ = 0 ⇒ θ = nπ 5) sinθ = sina⇒ θ = nπ + (-1)na where a ∈ [–π/2, π/2] 6) cosθ= cos a ⇒ θ = 2nπ ± a, where a ∈[0,π] 7) tanθ = tana⇒ θ = nπ+ a, where a ∈[–π/2, π/2] 8) sinθ = 1 ⇒ θ= (4n + 1)π/2 9) sin θ = -1 ⇒ θ = (4n - 1) π /2 10) sin θ = -1 ⇒ θ = (2n +1) π /2 11) |sinθ| = 1⇒ θ =2nπ 12) cosθ = 1 ⇒ θ =(2n + 1) 13) |cosθ| = 1⇒ θ =nπ #JEEHACKS

PRECAUTION: Each test tube containing the soap solution must be shaken with the same force and for the same period of time.

Sheet-17)KTG & Thermodynamics 👇👇👇👇👇👇👇

Sheet-16)Sound wave👇👇👇👇👇👇👇👇