Complete the following activity to find the value of x. - Vidyadip

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Complete the following activity to find the value of x.

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Activity:
$ \square=1+\tan ^2 \theta \quad \ldots . . .[\text { Fundamental trigonometric identity] }$
$\square-\tan ^2 \theta=1$
$(\sec \theta+\tan \theta) \cdot(\sec \theta-\tan \theta)=\square$
$\sqrt{3} \cdot(\sec \theta-\tan \theta)=1$
$(\sec \theta-\tan \theta)=\square $

In figure 3.95, chord EF || chord GH. Prove that, chord EG ≅ chord FH.
Fill in the blanks and write the proof.
Proof : Draw seg GF.
∠ EFG = ∠ FGH ...Alternate interior angles.......⬜(I)
∠ EFG = …………90° ………{inscribed angle theorem}(II)
∠ FGH = …………… 90° ………….{inscribed angle theorem} (III)
∴m(arc EG) = ……………90°…………. from (I), (II), (III).
chord EG ≅ chord FH ..........⬜

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Find distance between point $Q(3,-7)$ and point $R(3,3)$
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$NR =[\ldots] cm $

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70, 60, 50, 40, . . .
Here
$t_1$ = ⬜, $t_2$ = ⬜, $t_3$ = ⬜, ....
∴ a = ⬜, d = ⬜

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In figure 1.66, seg PQ || seg DE, A(Δ PQF) = 20 units, PF = 2 DP, then find A(DPQE) by completing the following activity.
A(Δ PQF) = 20 units, PF = 2 DP, Let us assume DP = x. ∴ PF = 2x
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In Δ FDE and Δ FPQ,
∠FDE ≅ ∠ .......... corresponding angles
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Adding the given equations,