Question

$\sqrt{\frac{1+sin\Theta}{1-sin\Theta} }$ is equal to
(a) sec θ + tan θ
(b) sec θ − tan θ
(c) sec²θ + tan²θ
(d) sec²θ− tan² θ

Answer 1

Answer:

√(1 + sinθ)/(1 − sinθ) = sec θ+ tan θ

Among the given options option (a) sec θ + tanθ is correct.  

Step-by-step explanation:

Given :

√(1 + sinθ)/(1 − sinθ)  

= √[(1 + sinθ) × √(1 + sinθ)] / [√(1 -sinθ) × √(1 + sinθ) ]  

[By rationalising]

= √(1 + sinθ)²/√(1 - sin²θ)

[By using an identity , (a + b) (a - b) = a² - b²]

= (1 + sinθ)/√cos²θ

[By using the identity, (1- sin²θ) = cos²θ

= (1 + sinθ)/cosθ

= 1/cosθ + sinθ/cosθ

= secθ + tanθ  

[By using , secθ = 1/ cosθ & tanθ = sinθ/cosθ]

√(1 + sinθ)/(1 − sinθ) = sec θ + tan θ

Hence, √(1 + sinθ)/(1 − sinθ) = sec θ + tan θ

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Answer:

a

Step-by-step explanation:

Just rationalise.

√ (1+sinθ) √(1+sinθ)

-------------- x ---------------

1 - sinθ (1+sinθ)

(1+sinθ)

= ---------------

cosθ

= secθ + tanθ