Mathematics - Class X Question Paper - Central Board Of Secondary Education Page 29
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33Q. No.
Value Points
Marks
Q17. Area of canvas required to build the tent
= curved surface area of cylindrical
part + curved surface of conical part
1
2
2
2
=169 Ü OA = 13 m
OA
=5
+12
1
∴ Required area = 2 πrh + πrl = πr(2h+l)
½
2
2
22
=
x 12(22+13) m
= 1320 m
1 ½
7
Q18. tan θ
cot θ
= 1 +sec θ cosec θ
+
1-cot θ
1-tan θ
tan θ
tan² θ
1
1
L.H.S
½+1
+
=
—
1- tan θ
tan θ (1 -tan θ)
tan θ (1 -tan θ)
1— 1
tan
θ
1 -tan³ θ
(1 — tan θ) (1 + tan θ + tan² θ
=
=
½+1
tan θ (1 - tan θ)
tan θ (1 — tan θ)
cos θ
sin θ
cotθ + 1+tanθ = 1 +
+
=1 + secθ cosecθ = R.H.S.
½+½
sin θ
cos θ
OR
0
0
0
cos 51
= cos(90-39)
= sin39
1
0
0
tan 79
= tan(90—11)
=
tan 11°
1
0
0
tan 59
= tan (90-31)
=
tan 31°
0
tan 45
= 1
0
0
0
sin 69
= sin(90-21)
= cos 21
2½
∴Given expression becomes
sin
1
1
+ 2 . tan 11° tan31° .1
.
—3 (sin² 21° + cos² 21°)
1
tan
tan 11°
39°
31°
sin 39°
= 1+2 —3 (1) = 0
½
164
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