Question

∆PQR is right Angeles at Q, Prove that: sin²R+cos²R=11​

Answer 1

Answer:

Step-by-step explanation:

In ΔPZX and ΔPQR

∠P=∠P        (∵common)

∠PZX=∠PQR=90°    (given)

By AA similarity  ΔPZX≈ΔPQR    →    (1)

In ΔXZQ and ΔPXQ

∠XZQ=∠PXQ     (90°each)

∠ZQX=∠PQX      (∵common)

By AA similarity, ΔXZQ≈ΔPXQ   →     (2)

In ΔPQR and ΔPXQ

∠PQR=∠PXQ    (∵each 90°)

∠P=∠P    (∵common)

By AA similarity,  ΔPQR ≈ΔPXQ  →      (3)

From eq (1),(2) and (3) transitivity property

ΔPZX≈ΔXZQ

Hence, AA similarity postulates,  

⇒  

ZX

PZ

​

=  

ZQ

ZX

​

⇒ZX  

2

=PZ×ZQ

Hence, proved