Question

if tan theta = 1/root3 , the value of cosec2 theta -sec2theta/cosec2theta +sec2theta

Answer 1

hey!!!

your answer is here...

given :-

tan ∅ = 1/√3

then value of cosec² ∅ - sec² ∅ / cosec² ∅ + sec² ∅

we know that tan = perpendicular/base

therefore tan ∅ = perpendicular/base

>> perpendicular = 1 and base = √3

>> hypotenuse = √ ( 1² + √3² )
= √ ( 1 + 3 )
= √4
= 2

therefore cosec ∅ = 2/1 and sec ∅ = 2/√3

>> cosec² ∅ - sec² ∅ / cosec² ∅ + sec² ∅
= (2/1)² - (2/√3)² / ( 2/1)² + (2/√3)²
= ( 4/1 - 4/3 ) / ( 4/1 + 4/3 )
= ( 12 /3 - 4/3 ) / ( 12/3 + 4/3 )
= ( 8/3 ) / ( 16/3 )
= 8/3 × 3/16
= 1/2

cheers!!!

Answer 2

answers is

1/2

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