Question

5) (sina - sinB)2 + (cosa - cosß)2 ;​

Answer 1

Ответ:

Объяснение:

(sina - sinB)² + (cosa - cosß)²=

=sin²a-2sinasinb+sin²b+cos²a-2cosacosb+cos²b=

=sin²a+cos²a + sin²b+cos²b -2(sinasinb+cosacosb)=

=1+1-2cos(a-b)=2-2cos(a-b)

Answer 2

It appears you have an expression involving trigonometric functions. Let's work with this expression step by step:

(1) (sinα - sinβ)^2 + (cosα - cosβ)^2

Now, you can expand and simplify each of these terms separately:

(2) (sinα - sinβ)^2 = sin^2(α) - 2sin(α)sin(β) + sin^2(β)

(3) (cosα - cosβ)^2 = cos^2(α) - 2cos(α)cos(β) + cos^2(β)

Now, we can combine these two simplified expressions:

(4) (sin^2(α) - 2sin(α)sin(β) + sin^2(β)) + (cos^2(α) - 2cos(α)cos(β) + cos^2(β))

Now, we can use the trigonometric identity sin^2(θ) + cos^2(θ) = 1:

(5) (1 - 2sin(α)sin(β) + 1) + (1 - 2cos(α)cos(β) + 1)

Simplify further:

(6) 2 - 2sin(α)sin(β) - 2cos(α)cos(β)

Now, you can factor out a 2 from each term:

(7) 2(1 - sin(α)sin(β) - cos(α)cos(β))

Now, you can use the trigonometric identity sin(α)sin(β) + cos(α)cos(β) = cos(α - β):

(8) 2(1 - cos(α - β))

So, the simplified expression for (sinα - sinβ)^2 + (cosα - cosβ)^2 is 2(1 - cos(α - β)).