Question

sec (3π/2- x) sec ( x - 5π/2 ) + tab (5π/2 +x) tanb(x 3π/2)​

Answer 1

Answer:

= sec (450° – θ) = sec[360° + (90° – θ)] sec (90° – θ) = cosec θRead more on Sarthaks.com - https://www.sarthaks.com/910187/prove-that-sec-3-2-sec-5-2-tan-5-2-tan-3-2-1?show=910197#a910197

Answer 2

Step-by-step explanation:

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$so \: here \: \: given \: trigonometric \: equation \: is \\ sec( \: 3\pi/2 - x).sec(x - 5\pi/2) + tan \: (5\pi/2 + x).tan \: (x - 3\pi/2) \\ so \: we \: know \: that \\ whenever \: there \: is \: \pi/2 \: \: the \: given \: trigonometric \: ratio \: changes \: to \: its \: complementary \: ratio \\ so \: complementary \: ratio \: of \: sec \: is \: cosec \: and \: similarly \: tan \: would \: get \: transformed \: into \: cot$

$hence \: then \\ = (cosec \: x.cosec \: x) - (cot \: x.cot \: x) \\ = -cosec {}^{2} x + cot {}^{2} x \\ = -1 \\ since \: \: 1 + cot {}^{2} x = cosec {}^{2} x$