Question

Help me solve this please ❤I will give the right answer brainliest ​

Answer 1

Step-by-step explanation:

√((1 + sin x) / (1 − sin x)) + √((1 − sin x) / (1 + sin x))

Square and take the square root.

√[√((1 + sin x) / (1 − sin x)) + √((1 − sin x) / (1 + sin x))]²

√[(1 + sin x) / (1 − sin x) + 2 + (1 − sin x) / (1 + sin x)]

Add the fractions using least common denominator.

√[((1 + sin x)² + (1 − sin x)²) / (1 − sin²x) + 2]

√[(1 + 2 sin x + sin²x + 1 − 2 sin x + sin²x) / (1 − sin²x) + 2]

√[(2 + 2 sin²x) / (1 − sin²x) + 2]

Use Pythagorean identity:

√[(2 + 2 sin²x) / (cos²x) + 2]

√[2 sec²x + 2 tan²x + 2]

√[2 sec²x + 2 (tan²x + 1)]

Use Pythagorean identity:

√[2 sec²x + 2 sec²x]

√[4 sec²x]

±2 sec x

If x is in the second quadrant, then sec x < 0.

-2 sec x