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Question

In a right angled triangle ABC right angled at B,
5×sinA=3.
Find the value of cosC + tanA + cosecC.

A
1215
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B
1312
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C
135
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D
125
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Solution

The correct option is C 135

Given, triangle ABC is right angled at B.
Also, 5×sinA=3

sinA=35=BCAC

Let BC = 3k, AC = 5k (BC:AC=3:5)

Applying Pythagoras theorem,
AB2+BC2=AC2AB2=(5k)2(3k)2=16k2AB=4k

cosC=BCAC=35tanA=BCAB=34cosecC=ACAB=54

Hence,
cosC+tanA+cosecC=35+34+54=12+15+2520=135

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