Question 142

If $$(1+ tan^{2} \theta) = \frac{625}{49}\ and\ \theta\ $$is acute, then what is the value of $$\ (\sqrt{sin \theta+cos\ \theta})\ $$?

Solution

Given,

$$(1+ tan^{2}\theta)$$ = $$\frac{625}{49}$$ (or) $$sec^{2}\theta$$ = $$\frac{625}{49}$$

$$sec\ \theta$$ = $$\frac{25}{7}$$

$$Cos\ \theta = \frac{7}{25}$$ and $$sin\ \theta = \frac{24}{25}$$

$$\ \sqrt{sin \theta+cos\ \theta}\ = \sqrt{\frac{7 + 24}{25}}$$ = $$\sqrt{\frac{31}{25}}$$ = $$\frac{\sqrt{31}}{5}$$

Hence, option C is the correct answer.

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