Question

COS 49° cos 41° - sin 49° sin 41° =_______​

Answer 1

Answer:

As we know that

sin(90°-α) = cosα

and, cos(90°-α) = sinα

∴(sin49°/cos41°)²+(cos41°/sin49°)²

=[sin(90°-41)/cos41°]² +[cos(90°-49°)/sin49°]²

=[cos41°/cos41°]² +[sin49°/sin49°]²

=1+1

=2

Answer 2

==> cos 49° cos 41° - sin 49° sin 41°

Let 49° = A and 41° = B

Then, the expression becomes

==> cos A cos B - sin A sin B

Which is equal to cos ( A + B )

==> cos ( 49° + 41° )

==> cos 90°

==> 0

Hence,

cos 49° cos 41° - sin 49° sin 41° = 0