Question

if cos x=-2/3 and pi<x<3pi/2 find the value of 4 tan^2x-5 cosec^2x​

Answer 1

Given as

cos x = -2/3 and π < x < 3π/2

As we know that in the third quadrant, tan x and cot x are positive and all other rations are negative.

Sin x = – √(1 - cos² x) = – √(1 -(-2/3) ² ) =

-0.7453559925

tan x = sin x / cosx = -0.7453559925/ (-2/3) = 1.11803398875

cosec x= 1/ sinx = 1/ -0.7453559925 = -1.3416407865

so , 4tan² x-5 cosec² x

= 4(1.11803398875)² - 5( -1.3416407865) ²

= - 4

Ans : . 4tan² x-5 cosec² x = - 4

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