How do you prove $sin (\frac{π}{2} - θ) = cos θ$ $sin(pi/2-theta) = cos theta$ ?

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How do you prove $sin (\frac{π}{2} - θ) = cos θ$ $sin(pi/2-theta) = cos theta$ ?

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Answer 1 · 2016-04-07T16:55:54

Use $sin (a - b) = sin a cos b - cos a sin b$ $sin(a-b)=sin a cos b - cos a sin b$ . Here, $a = \frac{π}{2} and b = θ . sin (\frac{π}{2}) = 1 and cos (\frac{π}{2}) = 0$ $a = pi/2 and b = theta. sin (pi/2)=1 and cos (pi/2)=0$ .

Explanation:

This way, you can prove all similar results, like, for example, $sin (π - θ) = sin θ$ $sin(pi-theta)=sin theta$ .

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How do you prove $sin (\frac{π}{2} - θ) = cos θ$ $sin(pi/2-theta) = cos theta$ ?

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How do you prove $sin (\frac{π}{2} - θ) = cos θ$ $sin(pi/2-theta) = cos theta$ ?