Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

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

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

If cosecx = 1 + cotx then x = 2nπ, 2nπ + `pi/2`

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

If tanθ + tan2θ + `sqrt(3)` tanθ tan2θ = `sqrt(3)`, then θ = `("n"pi)/3 + pi/9`

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

If tan(π cosθ) = cot(π sinθ), then `cos(theta - pi/4) = +- 1/(2sqrt(2))`.