Maharashtra State BoardHSC Arts 11th
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Question Bank Solutions for HSC Arts 11th - Maharashtra State Board - Mathematics and Statistics

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Mathematics and Statistics
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If A = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], then insert the appropriate symbol ∈ or ∉ in each of the following blank space: 

12 ...... A

[0.025] Sets and Relations
Chapter: [0.025] Sets and Relations
Concept: Sets and Their Representations

Answer the following:

If sinθ = `(x^2 - y^2)/(x^2 + y^2)` then find the values of cosθ, tanθ in terms of x and y.

[0.012] Trigonometry - 1
Chapter: [0.012] Trigonometry - 1
Concept: Introduction of Trigonometry

Prove the following:

`tan(pi/4 + theta) = (1 - tan theta)/(1 + tan theta)`

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Prove the following:

`((1 + tan x)/(1 - tan x))^2 = tan(pi/4 + x)/(tan(pi/4 - x))`

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Prove the following:

sin [(n + 1)A]. sin [(n + 2)A] + cos [(n + 1)A]. cos [(n + 2)A] = cos A

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Prove the following:

`sqrt(2)cos (pi/4 - "A")` = cos A + sin A

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Prove the following:

`(cos(x - y))/(cos(x + y)) = (cotx coty + 1)/(cotx coty - 1)`

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Prove the following:

`(cos15^circ - sin15^circ)/(cos15^circ + sin15^circ) = 1/sqrt(3)`

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find sin (A + B)

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find cos (A – B)

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find tan (A + B)

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

If tan A = `5/6, tan "B" = 1/11`, prove that A + B = `pi/4`

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Select the correct option from the given alternatives :

The value of sin(n + 1) A sin (n + 2) A + cos(n + 1) A cos(n + 2) A is equal to

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Select the correct option from the given alternatives :

If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = _____

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Select the correct option from the given alternatives :

The value of `costheta/(1 + sin theta)` is equal to ……

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Select the correct option from the given alternatives :

The numerical value of tan 20° tan 80° cot 50° is equal to ______.

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Prove the following:

If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Prove the following:

`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Prove the following:

tanA + tan(60° + A) + tan(120° + A) = 3 tan 3A

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles

Prove the following:

3tan610° – 27 tan410° + 33tan210° = 1

[0.013000000000000001] Trigonometry - 2
Chapter: [0.013000000000000001] Trigonometry - 2
Concept: Trigonometric Functions of Sum and Difference of Angles
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