HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`

In ΔABC, if a = 18, b = 24, c = 30 then find the values of A(ΔABC)

In ΔABC, if a = 18, b = 24, c = 30 then find the values of sinA.

In ΔABC prove that `(b + c - a) tan  "A"/(2) = (c + a - b)tan  "B"/(2) = (a + b - c)tan  "C"/(2)`.

In ΔABC prove that `sin  "A"/(2). sin  "B"/(2). sin  "C"/(2) = ["A(ΔABC)"]^2/"abcs"`

Find the principal value of the following: `sin^-1 (1/2)`

Find the principal value of the following: cosec^{- 1}(2)

Find the principal value of the following: tan^-1(– 1)

Find the principal value of the following: tan^{- 1}( - √3)

Find the principal value of the following: sin^-1 `(1/sqrt(2))`

Find the principal value of the following: cos^{- 1}`(-1/2)`

Evaluate the following:

`tan^-1(1) + cos^-1(1/2) + sin^-1(1/2)`

Evaluate the following:

`cos^-1(1/2) + 2sin^-1(1/2)`

Evaluate the following:

`tan^-1 sqrt(3) - sec^-1 (-2)`

Evaluate the following:

`"cosec"^-1(-sqrt(2)) + cot^-1(sqrt(3))`

Prove the following: 

`sin^-1(1/sqrt(2)) -3sin^-1(sqrt(3)/2) = -(3π)/(4)`

Prove the following:

`sin^-1(-1/2) + cos^-1(-sqrt(3)/2) = cos^-1(-1/2)`

Prove the following:

`sin^-1(3/5) + cos^-1(12/13) = sin^-1(56/65)`

Prove the following:

`cos^-1(3/5) + cos^-1(4/5) = pi/(2)`

Prove the following:

`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`