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+1 vote
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in Trigonometry by (44.9k points)
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If `tan theta=1/sqrt7`,then `(c o s e c^2theta-sec^2theta)/(c o s e c^2theta+sec^2theta)=?`
A. `(-2)/(3)`
B. `(-3)/(4)`
C. `(2)/(3)`
D. `(3)/(4)`

1 Answer

+1 vote
by (43.8k points)
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Best answer
Correct Answer - D
`tantheta=(1)/(sqrt(7))rArrcottheta=sqrt(7).`
`sec^(2)theta=(1+tan^(2)theta)=(1+(1)/(7))=(8)/(7)and "cosec"^(2)theta=(1+cot^(2)theta)=(1+7)=8.`
`therefore ("cosec"^(2)theta-sec^(2)theta)/("cosec"^(2)theta+sec^(2)theta)=((8-(8)/(7)))/((8+(8)/(7)))=(48)/(64)=(3)/(4).`

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