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Vvi objective 2023 mathematics for 12th

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12th crash course 2022-23
New batchs 11/11/2022
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12th CRASH COURSE
Beginners Batch start from 06/09/2022
By-Raghu sir

पढलो चाहे कही से, नंबर आयेगा यही से!

For class-11th, more useful formula 11th & 12th, jee, others
Mentor-Raghu Gupta
👉Important Concept to Solve a Specific Type of Question

If A + B = 90°

Results that are true always :

(i) sin A. sec B = 1 or sin A = cos B

(ii) cos A. cosec B = 1 or sec A = cosec B

(iii) tan A. tan B = 1 or tan A = cot B

(iv) cot A. cot B = 1

(v) sin²A + sin² B = 1

(vi) cos² A + cos² B = 1

👉👉Important Trigonometry Formula for Sum and Difference Of Two Angles

(1) sin (A+B) =sinA. cosB + cosA sinB

(2) sin(A – B) =sinA. cosB – cosA sinB

(3) cos(A+B) =cosA. cosB – sinA sinB

(4) cos(A-B) = cosA. cosB+sinA sinB

(5) 2 sinA.cosB = sin(A+B)+sin (A-B)

(6) 2 cosA. sinB = sin(A+B)-sin (A-B)

(7) 2 sinA. sinB = cos(A-B)-cos(A+B)

(8) 2 cosA.cosB = cos(A+B)+cos(A-B)

(9) sin²A-sin²B = sin(A+B). sin(A-B)

(10) cos²A-cos²B = cos(A+B).cos (A-B)

👉Trigonometry Formulas List
If A + B + C = 180°
Then, tan A+tanB+tanC = tan A. tan B.tan C

If A + B + C = 90°
Then, cot A + cot B + cot C = cot A cot B cot C

If (a) sin θ + cosec θ = 2,
then, sin⁴ θ + cosec⁴ θ = 2 or
sin² θ + cosec² θ = 2, i.e θ=90°

Trigonometry Maximum & Minimum Value
Maximum & Minimum Value

Minimum Maximum

sin θ, cos θ [odd power] –1
+1
sin θ, cos θ [even power] 0 +1
tan θ, cot θ [odd power] –∞ +∞
tan θ, cot θ [even power] 0 +∞
sec θ, cosec θ [odd power] –∞ +∞
sec θ, cosec θ [even power] +1 +∞
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RAGHU MATHEMATICS CLASSES
For-XI, XII, IIT-JEE, & B.sc(H),
Venue-maharajganj, Madhubani
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RMC मधुबनी, Result 2022
हम से नही हमारे छात्र-छात्राओं से पूछिए।