Question

lf cos (a-b)=cosA cos B+sinA sinB,find cos 15 and hence sin 75​

Answer 1

Answer:

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Step-by-step explanation:

cos(A−B)=cosAcosB+sinAsinB

Putting A=45 and B=30

We get cos(45−30)=cos45cos30+sin45sin30

cos15=  1/√2 * √3/2  +  1/√2 * 1/2

⇒cos15=  √3/2√2 + 1/2√2

= √3 + 1 / 2√2

sin(A−B) = sinAcosB−cosAsinB

Putting A=45 and B=30

We get sin(45+30)=sin45 cos30 + cos45 sin30

sin75 = √2/2 * √3/2 + √2/2 * 1/2

sin 75 = √6/4 + √2 / 4

= √6+√2/4