Question

in a quadrilateral abcd cosacosb+sincsind=??​

Answer 1

Given: A quadrilateral ABCD

To find: cos A cos B + sin C sin D = ?

Solution:

• Now we have given the quadrilateral ABCD.

• Consider the sum of adjacent angles is 180 degree, so:

              A + B = 180 and C + D = 180

• Now using these equations, we get:

              A + B = C + D

• Using cos on both sides, we get:

              cos( A + B) = cos(C + D)

• Now we know the formula:

              cos(x+y) = cos x cos y - sin x sin y

• Applying this, we get:

              cos A cos B - sin A sin B = cos C cos D - sin C sin D

              cos A cos B + sin C sin D = cos C cos D + sin A sin B

Answer:

        So the value of cos A cos B + sin C sin D is cos C cos D + sin A sin B