HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions

Find the value of `sin  (19pi^"c")/3`.

Find the value of :

cos 1140°

Find the values of:

`cot  (25pi^"c")/3`

Select the correct option from the given alternatives:

If secθ = m and tanθ = n, then `1/"m"{("m + n") + 1/(("m + n"))}` is equal to

Express the following as a sum or difference of two trigonometric function:

2 sin 4x cos 2x

Express the following as a sum or difference of two trigonometric function:

2 cos 4θ cos 2θ

Express the following as a sum or difference of two trigonometric function:

2 cos 35° cos 75°

Prove the following :

`(sin2x + sin2y)/(sin2x - sin2y) = (tan(x + y))/(tan(x - y))`

Prove the following :

sin 6x + sin 4x – sin 2x = 4 cos x sin 2x cos 3x

Prove the following :

`(sinx - sin3x + sin5x - sin7x)/(cosx - cos3x - cos5x + cos7x)` = cot2x

Prove the following :

sin 18° cos 39° + sin 6° cos 15° = sin 24° cos 33°

Prove the following :

cos 20° cos 40° cos 60° cos 80° = `1/16`

Prove the following :

sin 20° sin 40° sin 60° sin 80° = `3/16`

Prove the following:

cos 12°+ cos 84° + cos 156° + cos 132° = `-1/2`

Prove the following:

`(cos9x - cos5x)/(sin17x - sin3x) = - (sin2x)/(cos10x)`

Prove the following:

3(sin x – cos x)⁴ + 6(sin x + cos x)² + 4(sin⁶x + cos⁶x) = 13

Construct a matrix A = [a_ij]_{3 × 2} whose element a_ij is given by

a_ij = `(("i" - "j")^2)/(5 - "i")`

Construct a matrix A = [a_ij]_{3 × 2} whose element a_ij is given by

a_ij = i – 3j

Construct a matrix A = [a_ij]_{3 × 2} whose element a_ij is given by

a_ij = `(("i" + "j")^3)/5`

Calculate coefficient of variation of marks secured by a student in the exam, where the marks are: 85, 91, 96, 88, 98, 82