Question

Find the value of $\sin \theta \cos (90 - \theta ) + \cos \theta \sin (90 - \theta ) = $
$
  {\text{A}}{\text{. 0}} \\
  {\text{B}}{\text{. 1}} \\
  {\text{C}}{\text{. 2}} \\
  {\text{D}}{\text{. }}\dfrac{3}{2} \\
 $

Answer 1

Hint: Here we go through by the relation of complementary angles of trigonometric ratio. As we know the value of $\cos (90 - \theta )$and $\sin (90 - \theta )$by putting their value we get our result.

Complete step-by-step answer:
Here in the question we have to find the value of $\sin \theta \cos (90 - \theta ) + \cos \theta \sin (90 - \theta ) $
As we know that by the complementary angles of trigonometric ratio the value of $\cos (90 - \theta ) = \sin \theta $ and$\sin (90 - \theta ) = \cos \theta $.
By putting these values in the question we get,
$
   = \sin \theta \times \sin \theta + \cos \theta \times \cos \theta \\
   = {\sin ^2}\theta + {\cos ^2}\theta \\
 $
And we also know the trigonometric identity that the value of ${\sin ^2}\theta + {\cos ^2}\theta $ is 1.
=1
Hence option B is the correct answer.

Note: - Whenever you get this type of question the key concept to solve this is to learn about the complementary angles of trigonometric ratios and you have to also keep in mind supplementary angles of trigonometric ratios to solve such types of questions. And also learn about the trigonometric identities.