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

The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______

Find the principal solutions of cosec x = 2

Find the principal solutions of sin x − 1 = 0

Find the principal solutions of cos 2𝑥 = 1

Find the principal solutions of sin x = `-1/2`

Find the principal solutions of tan x = `-sqrt(3)`

If cos^–1x + cos^–1y – cos^–1z = 0, then show that x² + y² + z² – 2xyz = 1

Differentiate y = `sqrt(x^2 + 5)` w.r. to x

Differentiate y = e^tanx w.r. to x

If y = sin⁻¹ (2^x), find `("d"y)/(""d"x)` 

If f(x) is odd and differentiable, then f′(x) is

If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)` 

If y = `tan^-1[sqrt((1 + cos x)/(1 - cos x))]`, find `("d"y)/("d"x)`

Differentiate sin² (sin⁻¹(x²)) w.r. to x

Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x

Differentiate `sin^-1((2cosx + 3sinx)/sqrt(13))` w.r. to x

Differentiate `tan^-1((8x)/(1 - 15x^2))` w.r. to x

If y = `sqrt(cos x + sqrt(cos x + sqrt(cos x + ...... ∞)`, show that `("d"y)/("d"x) = (sin x)/(1 - 2y)`

If y = `sin^-1[("a"cosx - "b"sinx)/sqrt("a"^2 + "b"^2)]`, then find `("d"y)/("d"x)`

The slope of the tangent to the curve x = 2 sin³θ, y = 3 cos³θ at θ = `pi/4` is ______.