Q11 of 164 Page 41

If show that

Let the third side be p,

By Pythagoras theorem,

⇒ 5² + p² = 13²

⇒ 25 + p² = 169

⇒ p² = 144

⇒ p = 12

Therefore, the other angles are:

sin θ =

cos θ =

Putting these values in the left hand side:
⇒

⇒

⇒ 3

Which is equal to right hand side.

Hence proved.

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.

If show that

If prove that 1–2 sin²A = 2cos²A – 1.