If tanθ = 8/15, simplify θ - θ/²θ - θ

Correct Answer is : 11972119/7272119

Correct Answer is : 11972119/7272119

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JAMB Mathematics 2024 Paper

Question : 45

Total: 50

If tan

\theta

\frac{8}{15}

\frac{\sin\theta - \cos\theta}{\sin^2\theta - \sin\theta}

Solution:

Concept:

Use

\tan\theta

to find

\sin\theta

and

\cos\theta

from the sides of a right-angled triangle.

Explanation:

Since

\tan\theta = \frac{8}{15}

, the opposite side is

8

and the adjacent side is

15

Using Pythagoras theorem, the hypotenuse is

17

Therefore,

\sin\theta = \frac{8}{17}

and

\cos\theta = \frac{15}{17}

Now simplify the numerator:

\sin\theta - \cos\theta = \frac{8}{17} - \frac{15}{17} = -\frac{7}{17}

Next, simplify the denominator:

\sin^2\theta = \left(\frac{8}{17}\right)^2 = \frac{64}{289}

So,

\sin^2\theta - \sin\theta = \frac{64}{289} - \frac{8}{17} = \frac{64}{289} - \frac{136}{289} = -\frac{72}{289}

Thus,

\frac{\sin\theta - \cos\theta}{\sin^2\theta - \sin\theta} = \frac{-\frac{7}{17}}{-\frac{72}{289}} = \frac{7}{17} \times \frac{289}{72} = \frac{119}{72}

Answer:

\frac{119}{72}

(Option B)

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