General Aptitude TestQuantitative ReasoningTrigonometry

(1+sin θ)/(cos θ) is equal to which of the following (where θ ≠ (π)/2…

$\frac{1+\sin \theta}{\cos \theta}$ is equal to which of the following (where $\theta \neq \frac{\pi}{2}$) ?

Answer & explanation

Correct answer: option 4

Given :-

$\frac{1 + sin θ}{cos θ}$

Multiply and divide by ( 1 - sin θ )

= $\frac{1 + sin θ}{cos θ}$ × $\frac{1 - sin θ}{1 - sin θ}$

= $\frac{(1² - sin² θ}{cos θ ( 1 - sin θ)}$

= $\frac{(cos² θ}{cos θ ( 1 - sin θ)}$

= $\frac{(cos θ}{( 1 - sin θ)}$

So , Option 4 is correct .