Question

If sinP + sinQ = 7/5 an angle P + angle Q =90 degrees, without using a calculator determine the value of Sin2P

Answer 1

Given that,

• ∠P + ∠Q = 90°

⇒∠P = 90°-∠Q      or       ∠Q = 90°-∠P

• sinP + sinQ = 7/5

To find :

The value of sin2P.

Answer -

sinP + sinQ = 7/5

⇒sinP + sin(90°-P) = 7/5

⇒sinP + cosP = 7/5

(Squaring both sides :)

⇒sin²P + cos²P + 2 sinPcosP = 49/25

⇒1 + 2 sinPcosP = 49/25

(We know, 2 sinPcosP = sin2P)

⇒1 + sin2P = 49/25

⇒sin2P = 49/25 - 1

⇒sin2P = 24/25