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Question

What is the formula of 1-cosxsinx?


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Solution

Determine the formula of 1-cosxsinx.

It is known that 1-cos(2ΞΈ)=2sin2ΞΈ and sin(2ΞΈ)=2sinΞΈcosΞΈ.

So, 1-cosx=2sin2x2 and sinx=2sinx2cosx2.

Substitute the values into the expression 1-cosxsinxand simplify:

1-cosxsinx=2sin2x22sinx2cosx2β‡’1-cosxsinx=sinx2cosx2β‡’1-cosxsinx=tanx2

Hence, the formula for 1-cosxsinxistanx2.


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