Question 60

If $$\sec \theta = \frac{13}{5}, then \tan \theta - \sin \theta + \cos \theta$$ is equal to:

Solution

$$\sec\theta$$ = $$\frac{13}{5}$$

$$\cos\theta$$ = $$\frac{5}{13}$$

$$\sin\theta$$ = $$\sqrt{1- \cos^2 \theta}$$ = $$\sqrt{1- \frac{5}{13}^{2}}$$ = $$\frac{12}{13}$$

$$\tan\theta$$ = $$\frac {sin\theta}{cos\theta}$$ = $$\frac{12}{13} \div \frac{5}{13}$$ = $$\frac{12}{5}$$

$$\tan \theta - \sin \theta + \cos \theta$$ = $$\frac{12}{5}$$ - $$\frac{12}{13}$$ + $$\frac{5}{13}$$ = $$\frac{121}{65}$$

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