Question

Determine if the statement is true or false (Picture provided)

Answer 1

The answer is T (True)

Explanation:

From the figure we can see a right angled triangle.ΔABC

To find the trigonometric ratios

From the figure we can write,

Sin A = a/c

Cos B = a/c

Therefore Sin A = Cos B

Csc A = c/a

Sec B = c/a

Therefore Csc A = Sec B

Tan A = a/b

Cot B = a/b

Therefore Tan A = Cot B

Correct answer is true

Answer 2

True

Explanation:

By the definition,

`\sin A=\frac{\text{opposite leg}}{\text{hypotenuse}}=(BC)/(AB)=(a)/(c),\\ \\\cos B=\frac{\text{adjacent leg}}{\text{hypotenuse}}=(BC)/(AB)=(a)/(c)`

So,
`\sin A=\cos B.`

`\csc A=\frac{\text{hypotenuse}}{\text{opposite leg}}=(AB)/(BC)=(c)/(a),\\ \\\sec B=\frac{\text{hypotenuse}}{\text{adjacent leg}}=(AB)/(BC)=(c)/(a)`

Thus,
`\cos A=\sec B.`

`\tan A=\frac{\text{opposite leg}}{\text{adjacent leg}}=(BC)/(AC)=(a)/(b),\\ \\\cot B=\frac{\text{adjacent leg}}{\text{opposite leg}}=(BC)/(AC)=(a)/(b).`

Thus,
`\tan A=\cot B.`