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Question

ABC is a right angled triangle. Find the value of the
cosec2A+sin2Bcot2A.

A
0.0
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B
-1
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C
1
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D
2
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Solution

The correct option is D 2
cosecA=ACBC
cotA=ABBC
sinB=sin 90=1

cosec2A+sin2Bcot2A=AC2BC2+1AB2BC2
cosec2A+sin2Bcot2A=AC2BC2AB2BC2+1

cosec2A+sin2Bcot2A=AC2AB2BC2+1
Pythagoras Theorem in ABC
AB2+BC2=AC2
BC2=AC2AB2
So, cosec2A+sin2Bcot2A=BC2BC2+1

cosec2A+sin2Bcot2A=1+1=2

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