Question

If Sin (A + B) = Sin A× Cos B+ Cos A× Sin B. find the value of A snd B​

Answer 1

Answer:-

Hi ,

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sin( A + B ) = sinAcosB + cosAsinB

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1 ) Here , we assume

A = 45° , B = 30°

cos 15°

= cos ( 90 - 75 )

= sin 75 °

= sin ( 45 + 30 )

= sin45cos30 + cos45sin30

= ( 1/√2 )( √3/2 ) + ( 1/√2 ) ( 1/2 )

= ( √3/2√2) + 1/2√2

= ( √3 + 1 )/2√2

Therefore ,

cos15° = sin75° = ( √3 + 1 )/2√2

$\pink{\huge{\boxed{\mathfrak{ Hope \: its \: help \: You}}}}$

 

Answer 2

ANSWER

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$\bf{sin( A + B ) = sin \: A \: cos \: B + cos \: A \: sin \: B}$

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$\bf {1 ) Here , we \: assume }\\ \\ \bf{A = 45° , B = 30° } \\ \\ cos \: \bf{15° = cos( 90- 75 ) }\\ \\ \bf{= sin 75 °= sin ( 45 + 30 ) }\\ \\ \bf{ = sin \: 45 \: cos \: 30 + cos \: 45 \: sin \: 30 }\\ \\= ( 1/√2 )( √3/2 ) + ( 1/√2 ) ( 1/2 )\\ \\= ( √3/2√2) + 1/2√2 \\ \\ = ( √3 + 1 )/2√2$

$\bf{Hence}$

$\bf{cos \: 15° = sin \: 75° = ( √3 + 1 )/2√2} \:$