Is (1+sin(θ))(1-sin(θ))=cos^2(x) ?

The answer to whether (1+sin(θ))(1-sin(θ))=cos^2(x) is False

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prove (1+sin(θ))(1-sin(θ))=cos^2(x)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

θ = 0

For

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

plug in

x = 1

(1 + sin (0)) (1 - sin (0)) = 1

(1 + sin (0)) (1 - sin (0))

Use the following trivial identity:

sin (0) = 0

sin (0)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= (1 + 0) (1 - 0)

Simplify

= 1

cos^{2} (1) = 0.29192 \dots

cos^{2} (1)

Refine to a decimal form

= 0.29192 \dots

The two sides are not equal

\Rightarrow False

Is (1+sin(θ))(1-sin(θ))=cos^2(x) ?
The answer to whether (1+sin(θ))(1-sin(θ))=cos^2(x) is False