Answer: The correct option is (a), i.e., cos B= sin A.
Explanation:
It is given that the ∠B = ∠C and ∠D is a right angle.
Since two corresponding angles of both triangles are same, so by angel sum property three angles are also equal. Therefore by AAA rule both triangles are similar.
It is given that,
[tex]\angle B=\angle C[/tex]
[tex]\cos B=\cos C[/tex]
Using angle sum property angle C is written as,
[tex]\cos B=\cos (180-\angle D-\angle A)[/tex]
[tex]\cos B=\cos (180-90-\angle A)[/tex]
[tex]\cos B=\cos (90-\angle A)[/tex]
By using quadrant concepts.
[tex]\cos B=\sin A[/tex]
Therefore option A is correct.
