Question

C) cos2a + sin^2ae) sin^2a•ctg a / sin 2a​

Answer 1

Ответ:

Объяснение:

с)  =cos^2a -sin^2a+sin^2a =cos^2a

e) = sin^2a*cosa/sina : 2sina*cosa =sina*cosa/2sina*cosa =1/2

Answer 2

It seems like you've provided two trigonometric expressions labeled as "C)" and "e)". I'll go through both of them:

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

This expression involves the trigonometric functions cosine and sine. We can simplify it as follows:

Using the trigonometric identity: sin^2(a) + cos^2(a) = 1

Replace cos^2(a) with 1 - sin^2(a): cos(2a) + sin^2(a) = cos(2a) + 1 - sin^2(a) = 1 + cos(2a) - sin^2(a)

So, the simplified form of the expression is: 1 + cos(2a) - sin^2(a).

e) sin^2(a) • ctg(a) / sin(2a)

Let's break this down step by step:

• sin^2(a) is the square of the sine of angle "a".
• ctg(a) is the cotangent of angle "a", which is the reciprocal of the tangent: ctg(a) = 1 / tan(a).
• sin(2a) is the sine of angle "2a".

So, the expression can be written as:

sin^2(a) • ctg(a) / sin(2a) = sin^2(a) • (1 / tan(a)) / sin(2a)

Since tan(a) = sin(a) / cos(a), and ctg(a) = 1 / tan(a), we can further simplify:

sin^2(a) • ctg(a) / sin(2a) = sin^2(a) • (cos(a) / sin(a)) / sin(2a)

Cancel out common terms: = cos(a) / sin(2a)

So, the simplified form of the expression is: cos(a) / sin(2a).

Please note that these are the simplified forms of the given expressions, assuming that no additional restrictions are placed on the values of "a" to make the calculations more manageable.