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

If acos2θ + bsin2θ = c has α and β as its roots, then prove that tanα + tanβ = `(2b)/(a + c)`.

`["Hint: Use the identities" cos2theta = (1 - tan^2theta)/(1 + tan^2theta) "and" sin2theta =  (2tantheta)/(1 + tan^2theta)]`.

If θ lies in the first quadrant and cosθ = `8/17`, then find the value of cos(30° + θ) + cos(45° – θ) + cos(120° – θ).

Find the value of the expression `cos^4  pi/8 + cos^4  (3pi)/8 + cos^4  (5pi)/8 + cos^4  (7pi)/8`

[Hint: Simplify the expression to `2(cos^4  pi/8 + cos^4  (3pi)/8) = 2[(cos^2  pi/8 + cos^2  (3pi)/8)^2 - 2cos^2  pi/8 cos^2  (3pi)/8]`

If tanθ = `1/2` and tanΦ = `1/3`, then the value of θ + Φ is ______.

The value of `(1 - tan^2 15^circ)/(1 + tan^2 15^circ)` is ______.

The value of cos12° + cos84° + cos156° + cos132° is ______.

The value of `sin  pi/10  sin  (13pi)/10` is ______.

`["Hint: Use"  sin18^circ = (sqrt5 - 1)/4 "and"  cos36^circ = (sqrt5 + 1)/4]`

The value of sin50° – sin70° + sin10° is equal to ______.

If sinθ = `(-4)/5` and θ lies in the third quadrant then the value of `cos  theta/2` is ______.

The value of `sin  pi/18 + sin  pi/9 + sin  (2pi)/9 + sin  (5pi)/18` is given by ______.

If A lies in the second quadrant and 3tanA + 4 = 0, then the value of 2cotA – 5cosA + sinA is equal to ______.

The value of cos²48° – sin²12° is ______.

[Hint: Use cos²A – sin² B = cos(A + B) cos(A – B)]

The value of `(sin 50^circ)/(sin 130^circ)` is ______.

If k = `sin(pi/18) sin((5pi)/18) sin((7pi)/18)`, then the numerical value of k is ______.

If tanA = `(1 - cos "B")/sin"B"`, then tan2A = ______.

How many elements has \[P \left( A \right), \text{ if } A = \phi\]

If in ∆ABC, ∠A = 45°, ∠B = 60° and ∠C = 75°, find the ratio of its sides. 

If in ∆ABC, ∠C = 105°, ∠B = 45° and a = 2, then find b. 

In ∆ABC, if a = 18, b = 24 and c = 30 and ∠c = 90°, find sin A, sin B and sin C. 

In triangle ABC, prove the following: