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Maths Notes 11th 12th JEE
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Kanal postlari
Repost from Physics Notes Class 11th 12th
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| 3 | ➖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 | 2 256 |
| 4 | Now forward this message to my pm or click on the below button to connect!
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| 5 | /connect | 0 |
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| 8 | 🚨 Results are OUT!!
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| 9 | 🚨 Results are OUT!!
😵 Panic hokar galat college mat choose kar lena.
Aaj hi register kro to Scaler School of Technology 🚀 aur pao chance to win Scholarship upto 100%🎓💰
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Code:-TEST500
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| 10 | +3 6. xi liner equation maths notes A.pdf | 4 023 |
| 11 | 5 . xi quadratic equation part 1 maths A notes.pdf | 3 889 |
| 12 |  🚨 *Scaler School of Technology’s* May Intake Closes Tonight!
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| 13 | +1 6. xi liner equation maths notes A.pdf | 0 |
| 14 | 5 . xi quadratic equation part 1 maths A notes.pdf | 0 |
| 15 |  🚨 Scaler School of Technology's May Intake Closes Tomorrow 🚨
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Just a heads up that the application deadline for Scaler School of Technology is tomorrow ⏳ and I feel all of you should apply for NSET, their dedicated entrance test 🧠💻
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Quick note for JEE students 📚: If you scored 92%ile or above 🎯, you can skip the NSET exam entirely and go straight to the interview round 💯, with a chance to get up to 100% scholarship 🎓🔥 | 0 |
| 16 |  🚨🚨 2 days Left Only! Still stuck on JEE? 🚨🚨
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| 17 | +3 1.xi sets maths notes A.pdf | 3 945 |
| 18 | +5 8. xii application of integral maths notes.pdf | 4 912 |
| 19 | 13. xii Probability maths notes.pdf | 0 |
| 20 | +4 8. xii application of integral maths notes.pdf | 0 |
