a2linetagadaW
2020-10-23
Answered

Determine whether the statement "I’ve noticed that for sine, cosine, and tangent, the trig function for the sum of two angles is not equal to that trig
function of the first angle plus that trig function of the second angle", makes sense or does not make sense, and explain your reasoning.

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broliY

Answered 2020-10-24
Author has **97** answers

The statement is “ The trigonometric function for the sum of two angles is not equal to the trigonometric function of the first angle plus trigonometry function of the second angle.”
i.e. in a mathematical way, we can say

$\mathrm{sin}(A+B)\ne \mathrm{sin}\left(A\right)+\mathrm{sin}\left(B\right)$

$\mathrm{cos}(A+B)\ne \mathrm{cos}\left(A\right)+\mathrm{cos}\left(B\right)$

$\mathrm{tan}(A+B)\ne \mathrm{tan}\left(A\right)+\mathrm{tan}\left(B\right)$

The statement is True.

Since the formulas for the trigonometric function of the sum of two angles are

$\mathrm{sin}(A+B)=\mathrm{sin}\left(A\right)\mathrm{cos}\left(B\right)+\mathrm{cos}\left(A\right)\mathrm{sin}\left(B\right)$

$\mathrm{cos}(A+B)=\mathrm{cos}\left(A\right)\mathrm{cos}\left(B\right)+\mathrm{sin}\left(A\right)\mathrm{sin}\left(B\right)$

$\mathrm{tan}(A+B)=\frac{\mathrm{tan}\left(A\right)+\mathrm{tan}\left(B\right)}{1-\mathrm{tan}\left(A\right)\mathrm{tan}\left(B\right)}$

Hence generally the trigonometric function for the sum of two angles is not equal to the trigonometric function of the first angle plus trigonometry function of the second angle.

The statement is True.

Since the formulas for the trigonometric function of the sum of two angles are

Hence generally the trigonometric function for the sum of two angles is not equal to the trigonometric function of the first angle plus trigonometry function of the second angle.

Jeffrey Jordon

Answered 2021-12-14
Author has **2262** answers

Answer is given below (on video)

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