Question

Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.COS(30°) cos(45") + sin(30°)sin(45)

Answer 1

Remember that

$\cos (a+b)=\cos a\cdot\cos b+\sin a\cdot\sin b$

therefore

a=30 degrees

b=45 degrees

so

$\cos (30^o+45^o)=\cos (75^o)=\cos 30^o\cdot\cos 45^o+\sin 30^o\cdot\sin 45^o$