English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

If cos (81 + θ)° = sin`("k"/3 - theta)^circ` where θ is an acute angle, then the value of k is ______.

3 sin² 20° – 2 tan² 45° + 3 sin² 70° is equal to ______.

If sin 2A = `1/2` tan² 45° where A is an acute angle, then the value of A is ______.

`(sin theta)/(1 + cos theta)` is ______.

If x sin (90° – θ) cot (90° – θ) = cos (90° – θ), then x is equal to ______.

The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is ______.

If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to ______.

If sin θ + sin² θ = 1, then cos² θ + cos⁴ θ = ______.

5 tan² A – 5 sec² A + 1 is equal to ______.

If cos A = `4/5`, then the value of tan A is ______.

If sin A = `1/2`, then the value of cot A is ______.

Given that sinα = `1/2` and cosβ = `1/2`, then the value of (α + β) is ______.

The value of the expression `[(sin^2 22^circ + sin^2 68^circ)/(cos^2 22^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin 27^circ]` is ______.

Prove the following:

If tan A = `3/4`, then sinA cosA = `12/25`

If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.

The value of the expression (sin 80° – cos 80°) is negative.

A ladder rests against a vertical wall at an inclination α to the horizontal. Its foot is pulled away from the wall through a distance p so that its upper end slides a distance q down the wall and then the ladder makes an angle β to the horizontal. Show that `p/q = (cos β - cos α)/(sin α - sin β)`

`sqrt(3)` cos²A + `sqrt(3)` sin²A is equal to ______.

Prove that `tan θ/(1 - cot θ) + cot θ/(1 - tanθ)` = 1 + sec θ cosec θ

If sin θ + cos θ = `sqrt(2)` then tan θ + cot θ = ______.