Question

Упростить выражение 1- 1/cos^2a

Answer 1

1 - 1/cos²a =
Приводим в общему знаменателю:
(cos²a -1)/ cos²a =
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Основное тригонометрическое тождество:
sin²a + cos²a = 1
- sin²a = cos²a -1
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-sin²a/ cos²a= - tg²a
Ответ: -tg²a

Answer 2

1 - 1/cos^2a = (cos^2a-1)/cos^2a= -sin^2a/cos^2a= -tg^2a

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Answer 3

To simplify the expression 1 - 1/cos^2(a), we can use the trigonometric identity:

1 - 1/cos^2(a) = sin^2(a)

This identity is derived from the Pythagorean trigonometric identity:

sin^2(a) + cos^2(a) = 1

Dividing both sides by cos^2(a):

sin^2(a)/cos^2(a) + cos^2(a)/cos^2(a) = 1/cos^2(a)

sin^2(a)/cos^2(a) + 1 = 1/cos^2(a)

Now, recall that:

sin^2(a)/cos^2(a) = tan^2(a)

Substitute tan^2(a) back into the equation:

tan^2(a) + 1 = 1/cos^2(a)

Finally, we can rearrange the equation to get the simplified expression:

1 - 1/cos^2(a) = tan^2(a)