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प्रश्न
If `tan θ = 1/sqrt(7)` then prove that `(("cosec"^2θ + sec^2θ))/(("cosec"^2θ - sec^2θ)) = 4/3`.
सिद्धांत
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उत्तर
Given: `tan θ = 1/sqrt(7)`
To prove: `(("cosec"^2θ + sec^2θ))/(("cosec"^2θ - sec^2θ)) = 4/3`
Proof:
sec2θ = (1 + tan2θ)
= `(1 + 1/7)`
= `8/7`
cosec2θ = (1 + cot2θ)
= (1 + 7)
= 8
∴ `(("cosec"^2θ + sec^2θ))/(("cosec"^2θ - sec^2θ)) = ((8 + 8/7))/((8 - 8/7))`
= `64/48`
= `4/3`
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