Question

Cos a×sin a×tg a+cos^2 a

Answer 1

Вот тут всё по основному тригонометрическому тождеству

Answer 2

It appears that you have provided an expression involving trigonometric functions. The expression you've given is:

cos(a) × sin(a) × tan(a) + cos^2(a)

Let's break this down step by step:

1. cos(a) is the cosine of angle "a."
2. sin(a) is the sine of angle "a."
3. tan(a) is the tangent of angle "a."
4. cos^2(a) is the square of the cosine of angle "a."

To simplify this expression, we can use trigonometric identities:

• Recall that sin(a) / cos(a) = tan(a), which means sin(a) = tan(a) × cos(a).
• Also, cos^2(a) is equivalent to (cos(a))^2.

Now, let's substitute these identities into the expression:

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

Next, distribute the cos(a) on the left side:

cos(a) × tan(a) × cos(a) + (cos(a))^2

Now, let's simplify further:

• cos(a) × cos(a) = (cos(a))^2
• cos(a) × tan(a) is the same as sin(a), so it becomes sin(a).

So, the simplified expression is:

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

This is the simplified form of the expression you provided.