Is (1+cos(θ))/(csc(θ))=sin(θ)+cos(θ) ?

The answer to whether (1+cos(θ))/(csc(θ))=sin(θ)+cos(θ) is False

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prove (1+cos(θ))/(csc(θ))=sin(θ)+cos(θ)

prove

\frac{1 + cos ( θ )}{csc ( θ )} = sin (θ) + cos (θ)

False

Solution steps

\frac{1 + cos ( θ )}{csc ( θ )} = sin (θ) + cos (θ)

Show that the two sides are not equal

For

\frac{1 + cos ( θ )}{csc ( θ )} = sin (θ) + cos (θ)

plug in

θ = 1

\frac{1 + cos ( 1 )}{csc ( 1 )} = 1.29611 \dots

\frac{1 + cos ( 1 )}{csc ( 1 )}

Refine to a decimal form

= 1.29611 \dots

sin (1) + cos (1) = 1.38177 \dots

sin (1) + cos (1)

Refine to a decimal form

= 1.38177 \dots

The two sides are not equal

\Rightarrow False

sin^{2} (x) + 2 cos^{2} (x) = 1 + cos^{2} (x)

sin (2 θ) = 2 cos (θ) \cdot sin (θ)

\frac{1 + cos ( a )}{sin ( a )} = cot (\frac{a}{2})

csc (θ) sin (θ) = - \frac{8}{43}

csc (θ) sin (θ) - sin^{2} (θ) = cos^{2} (θ)

Is (1+cos(θ))/(csc(θ))=sin(θ)+cos(θ) ?
The answer to whether (1+cos(θ))/(csc(θ))=sin(θ)+cos(θ) is False