English Medium इयत्ता १० - CBSE Question Bank Solutions

If cosA + cos²A = 1, then sin²A + sin⁴A = 1.

(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec²θ.

The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.

Prove the following:

(sin α + cos α)(tan α + cot α) = sec α + cosec α

If `sqrt(3) tan θ` = 1, then find the value of sin²θ – cos²θ.

Simplify (1 + tan²θ)(1 – sinθ)(1 + sinθ)

If 2sin²θ – cos²θ = 2, then find the value of θ.

Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`.

Show that tan⁴θ + tan²θ = sec⁴θ – sec²θ.

If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.

If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p² – 1) = 2p.

If a sinθ + b cosθ = c, then prove that a cosθ – b sinθ = `sqrt(a^2 + b^2 - c^2)`.

Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`

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

Find the zeroes of the quadratic polynomial 6x² – 3 – 7x and verify the relationship between the zeroes and the coefficients.

If α and β are the zeros of a polynomial f(x) = px² – 2x + 3p and α + β = αβ, then p is ______.

If 5 tan β = 4, then `(5  sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.

If the zeroes of the polynomial x² + px + q are double in value to the zeroes of the polynomial 2x² – 5x – 3, then find the values of p and q.

Prove the following that:

`tan^3θ/(1 + tan^2θ) + cot^3θ/(1 + cot^2θ)` = secθ cosecθ – 2 sinθ cosθ

`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is ______.