Question

In the figure of ΔPQR , ∠P = θ°  and ∠R =∅° find
(i)  `sqrt(X +1) cot ∅`

(ii)`sqrt( x^3 + x ^2) tantheta`

(iii) cos θ 

Answer 1

In Δ𝑃𝑄𝑅, ∠𝑄 = 90⁰,
Using Pythagoras theorem, we get
𝑃𝑄 = `sqrt(PR^2 − QR^2)`
= `sqrt ((x + 2)^2 − x^2)`

= `sqrt(x^2 + 4x + 4 − x^2)`
= `sqrt(4 (x+ 1))`
= `2sqrt(x + 1)`
Now,

(i)  `(sqrt(x+1) cot theta`

=`(sqrt(x+1))xx(QR)/(PQ)`

=`(sqrt(x+1))xx x/(2 sqrt(x+1))`

=`x/2`

(ii) `(sqrt(x^3+x^2)) tan theta` 

= `(sqrt(x^2(x+1)))xx(QR)/(PQ)`

`=x sqrt((x+1))xx x/(2sqrt(x+1)`

= `x^2/2`

(iii) cos θ

=`(PQ)/(PR)   theta=(2sqrt(x+1))/(x+2)`