I) sin^2 a sec^2 b + tan^2 b cos^2 a = sin^2a + tan²b

Explanation:

sin² A sec² B + tan² B cos² A

A good first step is to write everything in terms of sine and cosine.

sin² A / cos² B + sin² B cos² A / cos² B

The fractions have the same denominator, so combine into one:

(sin² A + sin² B cos² A) / cos² B

Using Pythagorean identity, we can rewrite sin² B as 1 − cos² B:

(sin² A + (1 − cos² B) cos² A) / cos² B

Distribute:

(sin² A + cos² A − cos² B cos² A) / cos² B

Pythagorean identity:

(1 − cos² B cos² A) / cos² B

Now divide into two fractions again:

1 / cos² B − cos² B cos² A / cos² B

Simplify:

sec² B − cos² A

Using Pythagorean identity again:

(tan² B + 1) − (1 − sin² A)

tan² B + 1 − 1 + sin² A

tan² B + sin² A

answer: the direction of the wind is expressed as the direction from which the wind is blowing. for example, easterly winds blow from east to west, while westerly winds blow from west to east.

explanation:

. west