In triangle PQR, right angled at Q, if tan find the value of

(i) sin P cos R + cos P sin R

(ii) cos P cos R – sin P sin R.

Let the third side be p,

By Pythagoras theorem,

⇒ 1² + (√3)² = P²

⇒ 1 + 3 = p²

⇒ p² = 4

⇒ p = 2

Therefore, the other angles are:

sin P =

cos P =

sin R =

cos R =

(i) Putting the values in the expression:

sin P cos R + cos P sin R

⇒

⇒

⇒ 1

(ii) Putting the values in the expression:

cos P cos R – sin P sin R.

⇒

⇒ 0