Question

(1+tg^2a)*(1+cos^2a)

Answer 1

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

Answer 2

To simplify the expression (1 + tan^2(a))(1 + cos^2(a)), you can use trigonometric identities. Here's the step-by-step simplification:

1. Start with the given expression: (1 + tan^2(a))(1 + cos^2(a))

2. Use the identity tan^2(a) = sec^2(a) - 1: (1 + (sec^2(a) - 1))(1 + cos^2(a))

3. Distribute the terms in the first set of parentheses: ((1 - 1) + sec^2(a))(1 + cos^2(a))

4. Simplify the terms in the first set of parentheses: (0 + sec^2(a))(1 + cos^2(a))

5. Anything multiplied by 0 is 0, so the first part of the expression becomes 0: 0(1 + cos^2(a))

6. Anything multiplied by 0 is 0, so the entire expression simplifies to 0: 0

So, the simplified expression is 0.

Answer 3

To simplify the expression (1 + tan^2(a))(1 + cos^2(a)), you can use trigonometric identities to make the calculation easier. Here's the step-by-step simplification:

1. Start with the given expression:

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

2. Use the trigonometric identity for tangent:

tan^2(a) = sec^2(a) - 1

3. Substitute the identity into the expression:

(1 + (sec^2(a) - 1))(1 + cos^2(a))

4. Simplify further:

(1 - 1 + sec^2(a))(1 + cos^2(a))

Now, you have:

(sec^2(a))(1 + cos^2(a))

5. Use another trigonometric identity:

sec^2(a) = 1 + tan^2(a)

6. Substitute the identity into the expression:

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

And you're back to the original expression:

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

So, the simplified expression is the same as the original one.