Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

If 2 tan^–1(cos θ) = tan^–1(2 cosec θ), then show that θ = π 4, where n is any integer.

Show that `cos(2tan^-1  1/7) = sin(4tan^-1  1/3)`

Solve the following equation `cos(tan^-1x) = sin(cot^-1  3/4)`

Show that `sin^-1  5/13 + cos^-1  3/5 = tan^-1  63/16`

Prove that `tan^-1  1/4 + tan^-1  2/9 = sin^-1  1/sqrt(5)`

All trigonometric functions have inverse over their respective domains.

`"cos"  2 theta` is not equal to ____________.

When `"x" = "x"/2`, then tan x is ____________.

`"sin"^2 25° +  "sin"^2 65°` is equal to ____________.

If `"x + y" = "x"/4` then (1+ tanx)(1 + tany) is equal to ____________.

`("cos" 8° -  "sin" 8°)/("cos" 8° +  "sin" 8°)`  is equal to ____________.

`"sin"  265° -  "cos"  265°` is ____________.

I₂ is the matrix ____________.

Given that `"dy"/"dx"` = ye^x and x = 0, y = e. Find the value of y when x = 1.

Solve `x^2 "dy"/"dx" - xy = 1 + cos(y/x)`, x ≠ 0 and x = 1, y = `pi/2`

The integrating factor of the differential equation `"dy"/"dx" (x log x) + y` = 2logx is ______.

An appropriate substitution to solve the differential equation `"dx"/"dy" = (x^2 log(x/y) - x^2)/(xy log(x/y))` is ______.

Integrating factor of the differential equation `x "dy"/"dx" - y` = sinx is ______.

Integrating factor of the differential equation `"dy"/"dx" - y` = cos x is e^x.

One root of the equation `abs ((3"x" - 8, 3,3),(3, 3"x" - 8, 3),(3,3,3"x" - 8)) = 0` is ____________.