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प्रश्न
Find the other trigonometric functions:
If tan x = `(-5)/12`, x lies in the fourth quadrant.
उत्तर
Given, tan x = `-5/12`
We know that,
sec2x = 1 + tan2x
= `1 + (-5/12)^2`
= `1 + 25/144`
= `169/144`
∴ sec x = `± 13/12`
Since x lies in the 4th quadrant, sec x > 0
∴ sec x = `bb(13/12)`
cos x = `1/secx`
`= 1/(13/12)`
∴ cos x `bb(= 12/13)`
tan x = `sinx/cosx`
∴ sin x = tan x · cos x
= `-5/12 xx 12/13`
∴ sin x = `bb(-5/13)`
cosec x = `1/sinx`
= `1/((-5/13))`
= `1/sinx`
∴ cosec x = `bb(-13/5)`
cot x = `1/tanx`
= `1/((-5/12))`
∴ cot x = `bb(-12/5)`
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