HSC Science (General) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

Solve the triangle in which a = `(sqrt3 + 1)`, b = `(sqrt3 - 1)` and ∠C = 60°.

Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`

In any Δ ABC, prove the following:

a sin A - b sin B = c sin (A - B)

Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`

Evaluate the following:

`int (1)/sqrt((x - 3)(x + 2)).dx`

In any ΔABC, prove the following:

`("c" - "b cos A")/("b" - "c cos A") = ("cos B")/("cos C")`

Evaluate the following : `int (1)/(4 + 3cos^2x).dx`

In any Δ ABC, prove the following:

a² sin (B - C) = (b² - c²) sin A.

Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`

In any Δ ABC, prove the following:

ac cos B - bc cos A = a² - b²

Evaluate the following:

`int sinx/(sin 3x)  dx`

Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`

In any Δ ABC, prove the following:

`"cos 2A"/"a"^2 - "cos 2B"/"b"^2 = 1/"a"^2 - 1/"b"^2`

Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`

Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`

In any Δ ABC, prove the following:

`("b" - "c")/"a" = (tan  "B"/2 - tan  "C"/2)/(tan  "B"/2 +tan  "C"/2)`

Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`

Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`

In Δ ABC, if a, b, c are in A.P., then show that cot `"A"/2, cot  "B"/2, cot  "C"/2` are also in A.P.

Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`