Question

${cos}^{ - 1} \frac{1}{x} = {sec}^{ - 1} x \\ \\ proved$
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Answer 1

Step-by-step explanation:

${cos}^{ - 1} \frac{1}{x} = {sec}^{z - 1}x \\ \\ \bf\ r.h.s = \\ \\ \sf\ let \\ y = {sec}^{ - 1}x \\ \\ \sf\ \implies: x = sec \: y \\ \\\sf\ \implies: x = \frac{1}{cos \: y} \\ \\ \sf\ \implies: cos \: y = \frac{1}{x} \\ \\\sf\ \implies: y = {cos}^{ - 1} \frac{1}{x} \\ \\\sf\ \implies: {sec}^{ - 1}x = {cos}^{ - 1} \frac{1}{x} \\ \\ \tt\ \: l .h.s$

Answer 2

Answer:

(cos^-1)1/x=(sec^-1)x

solution✏

R.H.S

LET y=(sec^-1)x

=>x=sec y

=>x=1/cos y

=>cos y=1/x

=>y=(cos^-1)1/x

=>(sec^-1)x=(cos^-1)1/x

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