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

Prove the following identities.

cot θ + tan θ = sec θ cosec θ

Prove the following identities.

tan⁴ θ + tan² θ = sec⁴ θ – sec² θ

Prove the following identities.

`(1 - tan^2theta)/(cot^2 theta - 1)` = tan² θ

Prove the following identities.

`costheta/(1 + sintheta)` = sec θ – tan θ

Prove the following identities.

`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ

Prove the following identities.

`sqrt((1 + sin theta)/(1 - sin theta)) + sqrt((1 - sin theta)/(1 + sin theta))` = 2 sec θ

Prove the following identities.

sec⁶ θ = tan⁶ θ + 3 tan² θ sec² θ + 1

Prove the following identities.

(sin θ + sec θ)² + (cos θ + cosec θ)² = 1 + (sec θ + cosec θ)²

Prove the following identities.

sec⁴ θ (1 – sin⁴ θ) – 2 tan² θ = 1

Prove the following identities.

`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec"  theta - 1)/("cosec"  theta + 1)`

Prove the following identities.

`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`

Prove the following identities.

`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2

If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.

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