List of top Mathematics Questions asked in CBSE Class X

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\sqrt{\frac{\text{1 + sin A}}{\text{1 - sin A }}}= \text{sec A+ tan A}\)

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(\text{cos A - sin A + 1})}{\text{(cos A + sin A + 1)}} = \text{cosec A + cot A}\), using the identity cosec² A = 1 + cot² A.

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(1 + \text{sec A})}{\text{sec A}} = \frac{\text{sin² A}}{(\text{1 - cos A})}\) [Hint: Simplify LHS and RHS separately]

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: \(\frac{\text{cos A}}{(1 + \text{sin A})} + \frac{(1 +\text{ sin A})}{\text{cos A }}=\text{ 2 sec A}\)

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\( (\text{cosec θ}-\text{cot θ})²=\frac{(1-\text{cos θ})}{(1 +\text{cos θ})}\)

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.