Question

Sec θ = 20 /16 , then tanθ= what

Answer 1

Answer:

tanθ=3/4

Step-by-step explanation:

Given , secθ= 20/16

we know that

Sec²θ-tan²θ=1

and

$tanθ = \sqrt{ { \sec(θ) }^{2} - 1 }$

( on substituting the value of secθ we get)

$tanθ = \sqrt{( { \frac{20}{16} )}^{2} - 1 }$

$tanθ = \sqrt{( { \frac{400}{256} )} - 1 }$

on taking LCM we get,

$tanθ = \sqrt{( { \frac{400 - 256}{256}) } }$

on simplifying we get,

$tanθ = \sqrt{( { \frac{144}{256}) } }$

$tanθ = \sqrt{ {( \frac{12}{16}) }^{2} }$

$tanθ = {( \frac{12}{16}) }$

on futher simplification we get

$tanθ = \frac{3}{4}$

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