Respuesta :

Answer:

D - cos(157)

Step-by-step explanation:

Cos sum angle identity

cos(A+B) = cosAcosB - sinAsinB

103+54=157

Eduard22sly

The correct answer to the question is Cos 157

There are two ways to solve this question:

Method 1:

Evaluate: Cos103Cos54 – Sine103Sine54

This can be obtained as follow:

Cos103Cos54 – Sine103Sine54

= –0.1322 – 0.7883

= –0.9205

Next, we shall evaluate each option given in the question to see which will be equivalent to –0.9205. This is illustrated below:

Sine 49 = 0.7547

Cos 49 = 0.6561

Sine 157 = 0.3907

Cos 157 = –0.9205

From the above evaluation, we can see that Cos 157 is equivalent to Cos103Cos54 – Sine103Sine54

Thus, Cos 157 is the correct answer to the question.

Method 2

Again, we can apply the addition formula from trigonometry.

Cos (A – B) = CosACosB + SineASineB

Cos (A + B) = CosACosB – SineASineB

Sine (A + B) = SineACosB + SineBCosA

Sine (A – B) = SineACosB – SineBCosA

Comparing

Cos103Cos54 – Sine103Sine54 with the formula given above, it is very clear that:

Cos103Cos54 – Sine103Sine54 = Cos(103 + 54)

Cos103Cos54 – Sine103Sine54 = Cos 157

Recall:

Cos103Cos54 – Sine103Sine54 = –0.9205

Cos 157 =  –0.9205

Therefore, Cos 157 remains the correct answer to the question.

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