What is $sectheta+cos^2theta -costheta$ in terms of $sintheta$ ?

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Answer 1 · 2016-01-22T07:06:20

$=sin^2(theta)/sqrt(1-sin^2(theta)) + 1- sin^2(theta)$

$sec(theta) + cos^2(theta) - cos(theta)$

To simplify in terms of $sin(theta)$ let us write $sec(theta)$ as $1/cos(theta)$

$=1/cos(theta) + cos^2(theta) - cos(theta)$

$=1/cos(theta) + (cos^2(theta)cos(theta))/cos(theta) - (cos(theta)cos(theta))/cos(theta)$

$= (1+cos^3(theta)-cos^2(theta))/cos(theta)$

$=(1-cos^2(theta) + cos(theta)cos^2(theta))/cos(theta)$

$=(sin^2(theta)+sqrt(1-sin^2(theta))(1-sin^2(theta)))/sqrt(1-sin^2(theta)$

If you need it can be simplified further as

$=sin^2(theta)/sqrt(1-sin^2(theta)) + (sqrt(1-sin^2(theta))(1-sin^2(theta)))/sqrt(1-sin^2(theta)$

$=sin^2(theta)/sqrt(1-sin^2(theta)) + (cancel(sqrt(1-sin^2(theta)))(1-sin^2(theta)))/cancel(sqrt(1-sin^2(theta))$

$=sin^2(theta)/sqrt(1-sin^2(theta)) + 1- sin^2(theta)$

What is sectheta+cos^2theta -costhetasectheta+cos^2theta -costheta in terms of sinthetasintheta?