Explanation

We know secθ is the reciprocal of cosθ.  

So secθ = 1 / cosθ

Now multiply:

cosθ × secθ = cosθ × (1 / cosθ) = 1

The cosθ cancels out, and you are left with 1.

Last verified on 25-05-2026

Explanation

If sinθ = 20/29, use the identity sin²θ + cos²θ = 1.

First find sin²θ:

sin²θ = (20/29)² = 400/841

Now put in the identity:

400/841 + cos²θ = 1  

cos²θ = 1 - 400/841  

cos²θ = 841/841 - 400/841 = 441/841  

Take square root:

cosθ = 21/29  

So cosθ = 21/29.

Last verified on 25-05-2026

Explanation

If a = 10, then put it in the equation:

a² + b² = 200  

10² + b² = 200  

100 + b² = 200  

Subtract 100 from both sides:

b² = 200 - 100  

b² = 100  

So b = 10.

Last verified on 25-05-2026

Explanation

(12x + 8)/(x(x + 4)) = A/x + B/(x + 4)

Multiply both sides by x(x + 4):

12x + 8 = A(x + 4) + B(x)

Put x = 0:

12(0) + 8 = A(0 + 4) + B(0)

8 = 4A

A = 2

Put x = -4:

12(-4) + 8 = A(-4 + 4) + B(-4)

-48 + 8 = -4B

-40 = -4B

B = 10

Therefore:

(12x + 8)/(x(x + 4)) = 2/x + 10/(x + 4)

Last verified on 25-05-2026

Explanation

f(x) = x² - 4x

f(4) = 4² - 4(4) = 16 - 16 = 0  

f(2) = 2² - 4(2) = 4 - 8 = -4  

f(4) - f(2) = 0 - (-4) = 4

Last verified on 25-05-2026