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If `cos alpha=(2)/(3) and sin beta=(1)/(4)`, then find `cos(alpha-beta)`. |
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Answer» Given, `cos alpha=(2)/(3)implies sin alpha=(sqrt(5))/(3)` `sin beta=(1)/(4)implies cos beta=(sqrt(15))/(4)` `cos(alpha-beta)= cos alpha* cos beta+ sin alpha* sin beta=(2)/(3)xx(sqrt(15))/(4)+(sqrt(5))/(3)xx(1)/(4)` `cos(alpha-beta)=(2sqrt(15)+sqrt(5))/(12)`. |
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