Find the exact value of cos75^o

Solution:

Since 75^o = 45^o + 30^o, we have:

cos75^o

= cos(45^o+30^o)
= (cos45^o)(cos30^o) - (sin45^o)(sin30^o)

= (/2)(/2) - (/2)(1/2)

= ( - )/4

Example 2:

Find the exact value of sin15^o.

Solution:

We know that 15^o = 60^o - 45^o. Therefore we have:

sin15^o

= sin(60^o-45^o)
= (sin60^o)(cos45^o) - (sin45^o)(cos60^o)
= (/2)(/2) - (/2)(1/2)

= ( - )/4

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