SSLC (English Medium) Class 10 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`

If `(cos alpha)/(cos beta)` = m and `(cos alpha)/(sin beta)` = n, then prove that (m² + n²) cos² β = n²

If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1

If sin θ (1 + sin² θ) = cos² θ, then prove that cos⁶ θ – 4 cos⁴ θ + 8 cos² θ = 4

If `cos theta/(1 + sin theta) = 1/"a"`, then prove that `("a"^2 - 1)/("a"^2 + 1)` = sin θ

The value of sin²θ + `1/(1 + tan^2 theta)` is equal to 

tan θ cosec² θ – tan θ is equal to

If (sin α + cosec α)² + (cos α + sec α)² = k + tan²α + cot²α, then the value of k is equal to

If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a² – 1) is equal to

If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to 

If x = a tan θ and y = b sec θ then

a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p² – q² is equal to

Prove that `cot^2 "A" [(sec "A" - 1)/(1 + sin "A")] + sec^2 "A" [(sin"A" - 1)/(1 + sec"A")]` = 0

Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos²θ

Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`

If x sin³ θ + y cos³ θ = sin θ cos θ and x sin θ = y cos θ, then prove that x² + y² = 1

If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `±  sqrt("a"^2 + "b"^2 -"c"^2)`

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R₁ = {(2, 1), (7, 1)}

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R₂ = {(–1, 1)}

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R₃ = {(2, –1), (7, 7), (1, 3)}