Question

6) (1-cos 2a) tg (п+a)​

Answer 1

Відповідь:

1 - cos 2a = 2 sin^2 a

(1-cos 2a) tg (п+a) = 2 sin^2 a tg (п+a)

tg (a + b) = (tg a + tg b)/(1 - tg a tg b)

tg (п+a) = (tg п + tg a)/(1 - tg п tg a)

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

Удачи!

Покрокове пояснення:

Answer 2

To simplify the expression (1 - cos 2a) tan (π + a), we can use trigonometric identities. Let's break it down step by step:

Step 1: Use the double angle formula for cosine: cos 2a = 1 - 2sin²a

Step 2: Substitute the expression for cos 2a in the original expression: (1 - cos 2a) tan (π + a) = (1 - (1 - 2sin²a)) tan (π + a) = (2sin²a) tan (π + a)

Step 3: Use the identity for tangent of the sum of angles: tan (π + a) = -tan a

Step 4: Substitute the expression for tan (π + a) in the simplified expression: (2sin²a) tan (π + a) = (2sin²a)(-tan a) = -2sin²a tan a

So, the simplified expression is -2sin²a tan a.