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If 0ltxltpi/4andcosx+sinx=5/4, then the ...

If `0ltxltpi/4andcosx+sinx=5/4`, then the value of `16(cosx-sinx)^2` is ___________ .

Text Solution

Verified by Experts

The correct Answer is:
7
Let `y=cosx-sinx(ygt0)`
`y^2=1-2 sinx.cosx`
`cosx+sinx=5/4 ("Given")`
`:. 1+2 sinxcosx=25/16`
`or 2sinx.cosx=9/16`
Now `y^2=1-2sinxcosx=1-9/16=7/16`
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