SSLC (English Medium) कक्षा १० - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

A triangular shaped glass with vertices at A(– 5, – 4), B(1, 6) and C(7, – 4) has to be painted. If one bucket of paint covers 6 square feet, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied

Find the area of triangle AGF

Find the area of triangle FED

The area of triangle formed by the points (− 5, 0), (0, – 5) and (5, 0) is

A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y-axis. The path travelled by the man is

If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is

Find the area of a triangle formed by the lines 3x + y – 2 = 0, 5x + 2y – 3 = 0 and 2x – y – 3 = 0

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.