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Question

If A=130° and x=sinA+cosA, then,


A

x>0

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B

x<0

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C

x=0

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D

x0

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Solution

The correct option is A

x>0


Explanation for correct option:

Finding the value:

Given, A=130°

Now,

x=sinA+cosAx=sin130°+cos130°x=sin(180°50°)+cos(180°50°)x=sin50°cos50°x=sin50°cos(90°40°)x=sin50°sin40°....(1)

In equation

x=2sin(50°40°)2cos(50°+40°)2x=2sin5°cos45°sinCsinD=2sin(CD)2cos(C+D)2

As we know that sin5°&cos45° are positive,

Therefore, x is also positive & varies from x>0

Hence, correct option is (A)


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