Question

(sin(-a)+cos(pi+a))÷(1+2cos(pi÷2-a)cos(-a))

Answer 1

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Answer 2

Решение внизу на фото

Answer 3

Let's simplify the expression step by step:

1. Recall some trigonometric identities:

   • sin(-x) = -sin(x)
   • cos(-x) = cos(x)
   • cos(π/2 - x) = sin(x)
   • cos(π + x) = -cos(x)

2. Substitute the trigonometric identities into the expression:

   (sin(-a) + cos(π + a)) ÷ (1 + 2cos(π/2 - a)cos(-a))

3. Simplify further:

   (-sin(a) - cos(a)) ÷ (1 + 2sin(a)cos(a))

4. Combine the terms in the numerator:

   • (sin(a) + cos(a)) ÷ (1 + 2sin(a)cos(a))

5. Recognize the trigonometric identity:

   sin(2a) = 2sin(a)cos(a)

6. Substitute the identity into the expression:

   • (sin(a) + cos(a)) ÷ (1 + sin(2a))

And there you have it, the simplified expression is:

• (sin(a) + cos(a)) ÷ (1 + sin(2a))