1. ## trig result

Could I have help with the following

Simplify [1-sin(pi/2-2 theta)]/sin 2 theta

2. ## Re: trig result

Originally Posted by cos16mh
Could I have help with the following

Simplify 1-sin(pi/2-2 theta)/sin 2 theta
No definite answer; can be converted to different equivalent expressions.

e.g.

$1 - \frac {sin(\frac {\pi}{2} - 2\theta)}{sin 2\theta} = 1 - \frac {cos 2\theta}{sin 2\theta} = \frac {sin 2\theta - cos 2\theta}{sin 2\theta} \\ \\ = \frac {2sin \theta cos \theta - (cos^2 \theta - sin^2 \theta)}{2sin\theta cos\theta} \\ \\$

= . . etc . .

3. ## Re: trig result

Sorry all of 1-sin(pi/2-2theta is on the numerator

4. ## Re: trig result

Originally Posted by cos16mh
Could I have help with the following

Simplify [1-sin(pi/2-2 theta)]/sin 2 theta
That's why you gotta learn latex man.

$\frac{1-sin(\frac{\pi}{2}-2 \theta)}{sin(2 \theta)} = \\ \\ \frac{1-cos(2 \theta)}{sin(2 \theta)} = \frac{1-(1-2sin^2 \theta)}{sin(2 \theta)} \\ \\ = \frac{2sin^2 \theta}{2 sin \theta cos \theta} = \tan \theta$

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