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

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: 

In triangle ABC, prove the following: 

\[\left( a - b \right) \cos \frac{C}{2} = c \sin \left( \frac{A - B}{2} \right)\]

In triangle ABC, prove the following:

In triangle ABC, prove the following: 

In triangle ABC, prove the following: 

In any triangle ABC, prove the following: