List of top Mathematics Questions

Choose the correct option. Justify your choice. \(\frac{(1 + \text{tan}^2 A)}{(1 +\text{ cot}^ 2 A)}\)
Prove the following identities, where the angles involved are acute angles for which the expressions are defined: \(\frac{\text{tan θ}}{(\text{1 - cot θ})} + \frac{\text{cot θ}}{(\text{1 - tan θ})} = 1 + \text{secθ cosecθ}\) [Hint: Write the expression in terms of \(\text{sin θ}\) and \(\text{cos θ}\)]
Prove the following identities, where the angles involved are acute angles for which the expressions are defined: \(\frac{\text{cos A}}{(1 + \text{sin A})} + \frac{(1 +\text{ sin A})}{\text{cos A }}=\text{ 2 sec A}\)
Differentiate w.r.t. \(x\) the function: \((3x^2-9x+5)^9\)
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\( (\text{cosec θ}-\text{cot θ})²=\frac{(1-\text{cos θ})}{(1 +\text{cos θ})}\)
Differentiate the following w.r.t. x: \(e^{sin^{-1}x}\)
Differentiate the following w.r.t. x: \(\frac {e^x}{sin\ x}\)
Choose the correct option. Justify your choice. (sec A + tan A) (1 - sin A)
Choose the correct option. Justify your choice. \((1+\text{tan θ+sec θ}) (1+\text{cot θ - cosec θ}) =\)
Choose the correct option. Justify your choice. 9 sec2A - 9 tan2A =
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A
Write all the other trigonometric ratios of \(∠\) A in terms of sec A
State whether the following are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin \(\text{θ}\) increases as \(\text{θ}\) increases.
(iii) The value of cos \(\text{θ}\) increases as \(\text{θ}\) increases.
(iv) sin \(\text{θ}\) = cos \(\text{θ}\) for all values of \(\text{θ}\).
(v) cot A is not defined for A = 0°

In a classroom, 4 friends are seated at points A, B, C and D. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using the distance formula, find which of them is correct.
In a classroom, 4 friends are seated at points A, B, C and D.

If tan (A + B) = \(\sqrt3\) and tan (A - B) = \(\frac{1}{\sqrt3}\); 0°\( <\) (A + B) \(≤\) 90° ; A > B, find A and B
What is the maximum value of the function sin x + cos x?
Choose the correct option and justify your choice: \(\frac{2\ tan\ 30°}{1 - tan^2 30°} =\)
Choose the correct option and justify your choice: sin 2A = 2 sin A is true when A =
Choose the correct option and justify your choice: \(\frac{1 - tan^2 45°}{1 + tan^2 45°} =\)
Choose the correct option and justify your choice: \(\frac{2\ tan\  30°}{1 + tan^2 30°} =\)

Evaluate the following. 
(i) sin60° cos30° + sin30° cos 60°
(ii) 2tan245° + cos230° - sin260°
(iii) \(\frac{cos 45°}{sec 30°+cosec30°}\)


(iv) \(\frac{sin\ 30°+tan\ 45°cosec\ 60°}{sec\ 30°+cos\ 60°+cot\ 45°}\)


(v) \(\frac{5cos^260°+4sec^230°-tan^245°}{sin^230°+cos^230°}\)

If \(cot\  \theta = \frac{7}{8},\) evaluate:

(i) \(\frac{(1 + sin\  \theta)(1 – sin θ)}{(1+cos θ)(1-cos θ)}\)

(ii) \(cot^2\) \(θ\)

The graphs of \(y = p(x)\) are given in Fig. 2.10 below, for some polynomials \(p(x)\) . Find the number of zeroes of \(p(x)\), in each case
(I)
(ii)
(iii)
(iv)
(v)
(vi)
Prove that \(3 + 2\sqrt 5\) is irrational.
Prove that \(\sqrt 5\) is irrational.