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

Answer  the following questions in one word or one sentence or as per exact requirement of the question.

In a ∆ABC, if sinA and sinB are the roots of the equation  \[c^2 x^2 - c\left( a + b \right)x + ab = 0\]  then find \[\angle C\]  

Answer the following questions in one word or one sentence or as per exact requirement of the question.  

In ∆ABC, if a = 8, b = 10, c = 12 and C = λA, find the value of λ. 

Answer the following questions in one word or one sentence or as per exact requirement of the question. 

If the sides of a triangle are proportional to 2, \[\sqrt{6}\] and \[\sqrt{3} - 1\] find the measure of its greatest angle. 

Answer the following questions in one word or one sentence or as per exact requirement of the question.  

If in a ∆ABC, \[\frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c}\] then find the measures of angles A, B, C. 

Answer the following questions in one word or one sentence or as per exact requirement of the question. 

In any triangle ABC, find the value of \[a\sin\left( B - C \right) + b\sin\left( C - A \right) + c\sin\left( A - B \right)\ 

Answer the following questions in one word or one sentence or as per exact requirement of the question. 

In any ∆ABC, find the value of

\[\sum^{}_{}a\left( \text{ sin }B - \text{ sin }C \right)\]

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In any ∆ABC, \[\sum^{}_{} a^2 \left( \sin B - \sin C \right)\] = 

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In a ∆ABC, if a = 2, \[\angle B = 60°\]  and\[\angle C = 75°\] 

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If the sides of a triangle are in the ratio \[1: \sqrt{3}: 2\] then the measure of its greatest angle is 

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In any ∆ABC, 2(bc cosA + ca cosB + ab cosC) = 

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In a triangle ABC, a = 4, b = 3, \[\angle A = 60°\]   then c is a root of the equation 

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In a ∆ABC, if  \[\left( c + a + b \right)\left( a + b - c \right) = ab\] then the measure of angle C is 

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In any ∆ABC, the value of  \[2ac\sin\left( \frac{A - B + C}{2} \right)\]  is 

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In any ∆ABC, \[a\left( b\cos C - c\cos B \right) =\]  

Find the value of `(1 + cos  pi/8)(1 + cos  (3pi)/8)(1 + cos  (5pi)/8)(1 + cos  (7pi)/8)`

If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`, then find the value of xy + yz + zx.

If x = sec Φ – tan Φ and y = cosec Φ + cot Φ then show that xy + x – y + 1 = 0
[Hint: Find xy + 1 and then show that x – y = –(xy + 1)]