Is cos(pi-θ)+sin(pi/2+θ)=0 ?

The answer to whether cos(pi-θ)+sin(pi/2+θ)=0 is True

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prove cos(pi-θ)+sin(pi/2+θ)=0

prove

cos (π - θ) + sin (\frac{π}{2} + θ) = 0

True

Solution steps

cos (π - θ) + sin (\frac{π}{2} + θ) = 0

Manipulating left side

cos (π - θ) + sin (\frac{π}{2} + θ)

Rewrite using trig identities

= - cos (θ) + sin (\frac{π}{2} + θ)

Rewrite using trig identities

= - cos (θ) + cos (θ)

Add similar elements:

- cos (θ) + cos (θ) = 0

= 0

We showed that the two sides could take the same form

\Rightarrow True

sin (x) - csc (x) = - cos (x) cot (x)

tan (y) + cot (y) = sec (y) csc (y)

\frac{1}{sin ( x )} = csc (x)

\frac{csc ( θ )}{sec ( θ )} = cot (θ)

sec (x) csc (x) = tan (x) + cot (x)

Is cos(pi-θ)+sin(pi/2+θ)=0 ?
The answer to whether cos(pi-θ)+sin(pi/2+θ)=0 is True