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Question

ABDE is a trapezium with AEBD and EDBD, and AC is drawn parallel to the side DE.

Find the values of cot θ and cosec θ respectively, from the figure.


A

54,54

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B

2, 52

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C

43,53

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D

52, 2

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Solution

The correct option is C

43,53




Consider the figure ACDE
AECD and ACDE and ACCD

ACDE is a rectangle.

CD = AE = 10 units

BC = BD - CD = 16 - 10 = 6

Now, in ABC,

C=90

Now, from Pythagoras theorem,

AC2+BC2=AB2

AC2+62=102

AC=10036=8

cot θ=ACBC=86=43cosec θ=ABBC=106=53


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