Is tan(θ+pi/2)=-cot(θ) ?

The answer to whether tan(θ+pi/2)=-cot(θ) is True

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prove tan(θ+pi/2)=-cot(θ)

prove

tan (θ + \frac{π}{2}) = - cot (θ)

True

Solution steps

tan (θ + \frac{π}{2}) = - cot (θ)

Manipulating left side

tan (θ + \frac{π}{2})

Rewrite using trig identities

= - \frac{cos ( θ )}{sin ( θ )}

Use the basic trigonometric identity:

\frac{cos ( x )}{sin ( x )} = cot (x)

= - cot (θ)

We showed that the two sides could take the same form

\Rightarrow True

sin (B) + cos (B) cot (B) = csc (B)

3 sin (5 π - x) = 3 sin (x)

cos^{2} (θ) = \frac{1 + cos ( 2 θ )}{2}

1 - \frac{( sin ^{2} ( x ) )}{1 - cos ( x )} = - cos (x)

\frac{cos ^{2} ( α )}{1 - sin ( α )} = 1 + sin (α)