Question

Cos100°Cos40°+Sin100°Sin40°

Answer 1

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Answer 2

Step-by-step explanation:

Given :-

Cos100°Cos40°+Sin100°Sin40°

To find :-

Find the value of Cos100°Cos40°+Sin100°Sin40°?

Solution :-

Method-:1-

Given that

Cos100°Cos40°+Sin100°Sin40°

It is in the form of Cos A Cos B + Sin A Sin B

Where A = 100° and B = 40°

We know that

Cos (A-B) = Cos A Cos B + Sin A Sin B

=> Cos100°Cos40°+Sin100°Sin40°

=> Cos (100°-40°)

=> Cos 60°

=> 1/2

Method-2:-

Given that

Cos100°Cos40°+Sin100°Sin40°

=> Cos 100° Cos (90°-50°) + Sin 100°Sin(90°-50°)

We know that

Cos (90°-A) = Sin A

Sin (90°-A) = Cos A

=> Cos 100° Sin 50° + Sin 100° Cos 50°

=> Sin 50° Cos 100° + Cos 50° Sin 100°

It is in the form of Sin A Cos B + Cos A Sin B

Where , A = 50° and B = 100°

We know that

Sin (A+B) = Sin A Cos B + Cos A Sin B

=> Sin 50° Cos 100° + Cos 50° Sin 100°

=> Sin (50°+100°)

=> Sin 150°

=> Sin (90°+60°)

We know that

Sin (90°+A) = Cos A

=> Cos 60°

=> 1/2

Answer:-

The value of Cos100°Cos40°+Sin100°Sin40° is 1/2

Used formulae:-

→ Cos (90°-A) = Sin A

→ Sin (90°-A) = Cos A

→ Cos (A-B) = Cos A Cos B + Sin A Sin B

→ Sin (A+B) = Sin A Cos B + Cos A Sin B

→ Sin (90°+A) = Cos A