Question

Evaluate each of the following

4(sin⁴ 30° + cos² 60°) − 3(cos² 45° − sin² 90°) − sin² 60°

Answer 1

We have,

…… (1)

Now,

,, ,

So by substituting above values in equation (1)

We get,

LCM of 16 and 4 in the first term of above expression is 16 and

Similarly LCM of 2 and 1 in the second term of above expression is 2

Therefore,

Now in the second term of the above expression

Therefore,

Now, in the above expression 4 cancels 16 and 4 remains in the denominator of first term

Therefore,

Now by taking LCM =4 in the above expression

We get,

Now, in the above expression gets reduced to 2

Therefore,