Explanation

cotθ = 1/tanθ  

So:  

cotθ × tanθ = (1/tanθ) × tanθ = 1  

Last verified on 23-05-2026

Explanation

Given:  

cos θ = 9/41  

Use the formula:  

sin²θ + cos²θ = 1  

Step 1: Put cos θ value  

sin²θ + (9/41)² = 1  

sin²θ + 81/1681 = 1  

Step 2: Find sin²θ  

sin²θ = 1 - 81/1681  

sin²θ = 1681/1681 - 81/1681  

sin²θ = 1600/1681  

Step 3: Take square root  

sin θ = ±√(1600/1681)  

sin θ = ±40/41  

Last verified on 23-05-2026

Explanation

Given:  

a² + b² = 100  

a = 6  

Step 1: Put a = 6 in the equation  

6² + b² = 100  

36 + b² = 100  

Step 2: Solve for b²  

b² = 100 - 36

b² = 64  

Step 3: Take square root  

b = ±√64  

b = ±8  

So b = 8 or b = -8

Last verified on 23-05-2026

Explanation

(9x + 4) / [x(x + 4)] = A/x + B/(x + 4)

Multiply both sides by x(x + 4):

9x + 4 = A(x + 4) + B x

9x + 4 = A x + 4A + B x

9x + 4 = (A + B)x + 4A

Compare both sides:

4A = 4 => A = 1

A + B = 9 => 1 + B = 9 => B = 8

Therefore:

(9x + 4) / [x(x + 4)] = 1/x + 8/(x + 4)

Last verified on 23-05-2026

Explanation

f(x) = x² - 3

Find f(4):  

f(4) = 4² - 3 = 16 - 3 = 13

Find f(2):  

f(2) = 2² - 3 = 4 - 3 = 1

Now f(4) - f(2) = 13 - 1 = 12

Last verified on 23-05-2026