Commerce (English Medium) Class 11 - CBSE Question Bank Solutions

Find the general solution of the equation `(sqrt(3) - 1) costheta + (sqrt(3) + 1) sin theta` = 2

[Hint: Put `sqrt(3) - 1` = r sinα, `sqrt(3) + 1` = r cosα which gives tanα = `tan(pi/4 - pi/6)` α = `pi/12`]

If sinθ + cosecθ = 2, then sin²θ + cosec²θ is equal to ______.

If f(x) = cos²x + sec²x, then ______.

[Hint: A.M ≥ G.M.]

If tan θ = 3 and θ lies in third quadrant, then the value of sin θ  ______.

The value of tan 75° - cot 75° is equal to ______.

If tanα = `m/(m +  1)`, tanβ = `1/(2m + 1)`, then α + β is equal to ______.

The value of tan3A - tan2A - tanA is equal to ______.

The value of sin(45° + θ) - cos(45° - θ) is ______.

The value of `cot(pi/4 + theta)cot(pi/4 - theta)` is ______.

If tanA = `1/2`, tanB = `1/3`, then tan(2A + B) is equal to ______.

If sinθ + cosθ = 1, then the value of sin2θ is equal to ______.

If α + β = `pi/4`, then the value of (1 + tan α)(1 + tan β) is ______.

If tanα = `1/7`, tanβ = `1/3`, then cos2α is equal to ______.

If tanθ = `a/b`, then bcos2θ + asin2θ is equal to ______.

If sinx + cosx = a, then sin⁶x + cos⁶x = ______.

If sinx + cosx = a, then |sinx – cosx| = ______.

3(sinx – cosx)⁴ + 6(sinx + cosx)² + 4(sin⁶x + cos⁶x) = ______.

Given x > 0, the values of f(x) = `-3cos sqrt(3 + x + x^2)` lie in the interval ______.

The maximum distance of a point on the graph of the function y = `sqrt(3)` sinx + cosx from x-axis is ______.

State whether the statement is True or False? Also give justification.

If tanA = `(1 - cos B)/sinB`, then tan2A = tanB