Question

Cos A + B into Cos A minus b​

Answer 1

Ques. cos(A+B) cos(A−B) is equal to.

Answer:

Therefore, the required answer is $cos(A+B) cos(A-B) = cos^{2} A-sin^{2}B$.

Step-by-step explanation:

Concept:

There are six popular trigonometric functions for an angle. Sine ($sin$), cosine ($cos$), tangent ($tan$), cotangent ($cot$), secant ($sec$), and cosecant ($cosec$) are their respective names and acronyms. The three main trigonometry functions are sine, cosine, and tangent, while the other three are cotangent, secant, and cosecant. Equations involving trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.

Formulas used:

$cos(A+B)= cosAcosB-sinAsinB$

$cos(A-B)= cosAcosB+sinAsinB$

Given:

$cos(A+B) cos(A-B)$

To find:

We have to find the value of $cos(A+B) cos(A-B)$.

Solution:

It is given that,

$cos(A+B) cos(A-B)$

$=(cosAcosB-sinAsinB)(cosAcosB+sinAsinB)$

$=cos^{2} Acos^{2}B-sin^{2}Asin^{2}B$

$=cos^{2} A(1- sin^{2}B)-(1-cos^{2}A)-sin^{2}B$

$=cos^{2} A-sin^{2}B$

Hence, the required answer is $cos^{2} A-sin^{2}B$.

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Answer 2

Answer:

cos2A - sin2B.

Step-by-step explanation:

Ques. cos(A+B) cos(A-B)

Answer:

Therefore, the required answer is cos(A+B)cos(A-B) = cos A- sin B

There are six popular trigonometric functions for an angle. Sine (sin), cosine ( cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) are their respective names and acronyms. The three main trigonometry functions are sine, cosine, and tangent, while the other three are cotangent, secant, and cosecant. Equations involving trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities. Formulas used:

cos(A+B)= cos Acos B-sinAsinB

cos (A-B)=cos Acos B+ sin AsinB

Given:

cos (A+B)cos(A-B)

To find:

We have to find the value of cos(A+B)cos(A-B).

Solution:

It is given that,

cos(A+B)cos(A-B)

= (cos Acos B-sin Asin B) (cos AcosB+ sin AsinB)

=cos2 Acos2 B- sin² Asin2B

=cos2A(1-sin2B)-(1-cos2A) - sin²B

=cos A-sin2 B

Hence, the required answer is cos2A - sin2B.

cos2A - sin2B.

Is the correct answer of this question.

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