3 years ago

Prove csc(pi/2 -x) = sec x

Mathematics

1 answer:

kifflom [539]3 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

Consider the left side

Using the trigonometric identities

csc x = $\frac{1}{sinx}$ and sec x = $\frac{1}{cosx}$

Note that sin( $\frac{\pi }{2}$ - x) = cos x

Hence

csc( $\frac{\pi }{2}$ - x)

= $\frac{1}{sin(\frac{\pi }{2}-x) }$

= $\frac{1}{cosx}$

= sec x = right side ⇒ proven

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Read 2 more answers

The Johnson twins were born nine years after their older sister. This year, the product of the three siblings ages is exactly 18

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Answer: The age of the twins is 10 years.

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$x(x-9)(x-9)\\\\=x(x^2-18x+81)\\\\=x^3-18x^2+81x$

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According to question,

$1861+3x-18=x^3-18x^2+81x\\\\x^3-18x^2+81x-3x+18-1861=0\\\\x^3-18x^2+78x-1843=0\\\\x=19$

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