tan(π÷4-angle)+tan(3π÷4+angle)=0

Tan (π÷4-angle)+tan(3π÷4+angle)=0
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This is an identity, not an equation that you can solve for the angle.

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1 Answer

tan(A)=-tan(π-A) for all A because the tangent is negative in quadrants 2 and 4.

This is the same as tan(A)+tan(π-A)=0.

If A=π/4-x, where x is the angle, then tan(π/4-x)+tan(π-(π/4-x))=tan(π/4-x)+tan(3π/4+x)=0, proving the given identity.

 

by Top Rated User (1.2m points)

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