Question

(1 + tg² a) cos²a упрастить ​

Answer 1

По формуле 1 + tg²a= 1/cos²a.

(1 + tg² a) cos²a = 1/cos²a • cos²a= 1.

Ответ: 1

Answer 2

To simplify the expression (1 + tan²a) cos²a, we can start by using the trigonometric identity:

tan²a + 1 = sec²a

Replacing tan²a with sec²a - 1, we have:

(1 + tan²a) cos²a = (1 + sec²a - 1) cos²a

Simplifying the expression further:

= sec²a cos²a

Now, we can use another trigonometric identity:

sec²a = 1/cos²a

Substituting this into the expression, we get:

sec²a cos²a = (1/cos²a) cos²a

The cos²a terms cancel out, resulting in:

= 1

Therefore, the simplified form of (1 + tan²a) cos²a is 1.