English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to

If sin θ − cos θ = 0 then the value of sin⁴θ + cos⁴θ

The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to 

If cos  \[9\theta\] = sin \[\theta\] and  \[9\theta\]  < 90⁰ , then the value of tan \[6 \theta\] is

If  cos (\[\alpha + \beta\]= 0 , then sin \[\left( \alpha - \beta \right)\] can be reduced to  

Find A if tan 2A = cot (A-24°).

Find the value of ( sin² 33° + sin² 57°).

Prove that :(sinθ+cosecθ)²+(cosθ+ secθ)² = 7 + tan² θ+cot² θ.

Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2. 

Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`

Evaluate:
`(tan 65°)/(cot 25°)`

Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.

Prove that (sin θ + cosec θ)² + (cos θ + sec θ)² = 7 + tan² θ + cot² θ. 

If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)

Evaluate:

`(tan 65^circ)/(cot 25^circ)`

Prove that:
`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2 "cosec"θ`

Prove that:

`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`

Prove that: 2(sin⁶ θ + cos⁶ θ) – 3 (sin⁴ θ + cos⁴ θ) + 1 = 0.

A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.

There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.