Question #3fa40

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Question #3fa40

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Answer 1 · 2017-05-18T08:07:29

see below

Explanation:

${cos}^{2} X - {sin}^{2} X = 2 {cos}^{2} X - 1$ $cos^2 X - sin^2 X = 2 cos^2 X -1$

we use LHS to prove RHS
we know that,
${sin}^{2} X + {cos}^{2} X = 1$ $sin^2 X + cos^2 X = 1$ , then
${sin}^{2} X = 1 - {cos}^{2} X$ $sin^2 X = 1 - cos^2 X$

therefore
${cos}^{2} X - {sin}^{2} X = {cos}^{2} X - (1 - {cos}^{2} X)$ $cos^2 X - sin^2 X = cos^2 X - (1 - cos^2 X)$

${cos}^{2} X - {sin}^{2} X = {cos}^{2} X - 1 + {cos}^{2} X$ $cos^2 X - sin^2 X = cos^2 X -1 +cos^2 X$

${cos}^{2} X - {sin}^{2} X = 2 {cos}^{2} X - 1$ $cos^2 X - sin^2 X = 2cos^2 X -1$ -->proved

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Question #3fa40

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