Question

If sin (A + B) = Sin A cos B + cos A sin B, then find the value of cos 15° and sin 75°

Answer 1

(ii) Sin 75 = sin (45+30)
Sin ( 45 +30) = sin45 cos30 + cos45 sin30
                     = 1/√2 * √3/2 + 1√2* 1/2
                     = √3/2√2 + 1/ 2√2
                     = √3 +1 / 2√2
multiplying with √2,
(√3 + 1) * √2/ 2√2 *√2
= √6 + √2/ 4

(i) cos 15= cos(45-30)
   cos(45-30) = cos 45 cos30 - sin45 sin 30
                     = 1/√2 * √3/2 - 1√2 * 1/2
                     = √3 - 1/ 2√2
multiplying with √2,
(√3 - 1) * √2/ 2√2 *√2
= √6 - √2/ 4

hope it helps.... :)

Answer 2

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

I hope this helps you.

: )