Question

Evaluate each of the following

(cos 0° + sin 45° + sin 30°) (sin 90° − cos 45° + cos 60°)

Answer 1

We have,

…… (1)

Now,

,,

So by substituting above values in equation (1)

We get,

Now, LCM of both the product terms in the above expression is

Therefore we get,

Now by rearranging terms in the numerator of above expression

We get,

Now, by applying formula in the numerator of the above expression we get,

…… (2)

Now, we know that

Therefore,

Now, by substituting the above value of in equation (2)

We get,

Now gets reduced to

Therefore,

Hence,