HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

In ∆ABC, prove that `(cos^2"A" - cos^2"B")/("a" + "b") + (cos^2"B" - cos^2"C")/("b" + "c") + (cos^2"C" - cos^2"A")/("c" + "a")` = 0

In ΔABC, prove that `("a"^2sin("B" - "C"))/(sin"A") + ("b"^2sin("C" - "A"))/(sin"B") + ("c"^2sin("A" - "B"))/(sin"C")` = 0

In ΔABC, prove that `("b"^2 - "c"^2)/"a" cos"A" + ("c"^2 - "a"^2)/"b" cos"B" + ("a"^2 - "b"^2)/"c" cos "C"` = 0

In ∆ABC, if ∠A = `pi/2`, then prove that sin(B − C) = `("b"^2 - "c"^2)/("b"^2 + "c"^2)`

If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______

`int  ("e"^x(x - 1))/(x^2)  "d"x` = ______ 

`int sqrt(1 + sin2x)  dx`

`int (sin4x)/(cos 2x) "d"x`

`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`

`int logx/x  "d"x`

`int (2 + cot x - "cosec"^2x) "e"^x  "d"x`

`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`

`int ("e"^(2x) + "e"^(-2x))/("e"^x)  "d"x`

`int x^x (1 + logx)  "d"x`

`int 1/(xsin^2(logx))  "d"x`

`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`

`int (cos2x)/(sin^2x)  "d"x`

`int cot^2x  "d"x`

`int x/(x + 2)  "d"x`

`int cos^7 x  "d"x`