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

In triangle ABC, prove the following: 

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

In triangle ABC, prove the following: 

In triangle ABC, prove the following: 

In triangle ABC, prove the following: 

In triangle ABC, prove the following: 

In triangle ABC, prove the following: 

In triangle ABC, prove the following: 

In triangle ABC, prove the following: 

In triangle ABC, prove the following:

In triangle ABC, prove the following: 

In ∆ABC, prove that: \[a \sin\frac{A}{2} \sin \left( \frac{B - C}{2} \right) + b \sin \frac{B}{2} \sin \left( \frac{C - A}{2} \right) + c \sin \frac{C}{2} \sin \left( \frac{A - B}{2} \right) = 0\]

In ∆ABC, prove that: \[\frac{b \sec B + c \sec C}{\tan B + \tan C} = \frac{c \sec C + a \sec A}{\tan C + \tan A} = \frac{a \sec A + b \sec B}{\tan A + \tan B}\]

In triangle ABC, prove the following: 

\[a \left( \cos B \cos C + \cos A \right) = b \left( \cos C \cos A + \cos B \right) = c \left( \cos A \cos B + \cos C \right)\]

In ∆ABC, prove that \[a \left( \cos C - \cos B \right) = 2 \left( b - c \right) \cos^2 \frac{A}{2} .\] 

In ∆ABC, prove that if θ be any angle, then b cosθ = c cos (A − θ) + a cos (C + θ). 

In ∆ABC, if sin² A + sin² B = sin² C. show that the triangle is right-angled. 

In ∆ABC, if a², b² and c² are in A.P., prove that cot A, cot B and cot C are also in A.P. 

The upper part of a tree broken by the wind makes an angle of 30° with the ground and the distance from the root to the point where the top of the tree touches the ground is 15 m. Using sine rule, find the height of the tree. 

At the foot of a mountain, the elevation of it summit is 45°; after ascending 1000 m towards the mountain up a slope of 30° inclination, the elevation is found to be 60°. Find the height of the mountain.