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If x= sin130^@ + cos130^@ then 1.) x ...

If ` x= sin130^@ + cos130^@` then 1.) x < 0 2.) x = 0 3.) x > 0 4.) x`>= 0`

Text Solution

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`x = sin 130^@ + cos 130^@`
`=> x= sin(90^@+40^@)+cos(90^@+40^@)`
`=>x = cos40^@-sin40^@`
As we know, `sin 45^@ and cos45^@` are equal and for `theta lt 45^@`, value of `cos theta gt sin theta`,
`:. cos40^@-sin40^@ gt 0`
`:. x gt 0`
So, option `(3)` is the correct answer.
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