How do you simplify $tan t \cdot cot t - {sin}^{2} t$ $tan t * cot t - sin^2 t$ ?

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How do you simplify $tan t \cdot cot t - {sin}^{2} t$ $tan t * cot t - sin^2 t$ ?

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Answer 1 · 2015-09-01T20:03:26

${cos}^{2} t$ $cos^2t$

Explanation:

$tan t cot t = tan t x (\frac{1}{tan t}) = 1$ $tan tcot t= tan tx (1/tan t)=1$
$1 - {sin}^{2} t = ({sin}^{2} t + {cos}^{2} t) - {sin}^{2} t = {cos}^{2} t$ $1-sin^2t=(sin^2 t+cos^2 t)-sin^2 t=cos^2t$

Answer 2 · 2015-09-01T20:08:26

This problem requires some trigonometric identities,here,
1) cotx=1/tanx
2) ${sin}^{2} x$ $sin^2x$ + ${cos}^{2} x$ $cos^2x$ =1 or ${cos}^{2} x$ $cos^2x$ =1- ${sin}^{2} x$ $sin^2x$

Explanation:

1) tan t*cot t - ${sin}^{2} t$ $sin^2t$ * = tan t 1/tan t- ${sin}^{2} t$ $sin^2t$ ........(putting identity .1)
= 1- ${sin}^{2} t$ $sin^2t$ ................(putting identity .2)
= ${cos}^{2} t$ $cos^2t$
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I hope this helps :)

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How do you simplify $tan t \cdot cot t - {sin}^{2} t$ $tan t * cot t - sin^2 t$ ?

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