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Question

State whether the following statement is true or false.
If A,B,C are interior angles of ABC, then cosec(A+B2) =sec (C2) .

A
True
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B
False
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Solution

The correct option is A True

Here, ABC is a triangle and A,B,C are interior angles of the triangle.

A+B+C=180o [ Angle sum property of a triangle ]

A+B=180oC

Dividing both sides by 2 we get,

A+B2=180o2C2

A+B2=90oC2

Multiplying both sides by cosec we get,

cosec(A+B2)=cosec(90oC2)
We know, cosec(90oθ)=secθ

cosec(A+B2)=sec(C2) ------ Hence proved


1458113_1329378_ans_6e5ca9b37eba487aa5b2a9e0a8f793fe.png

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