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प्रश्न
Evaluate the following: `((1 - cosθ)(1 + cosθ))/((1 - sinθ)(1 + sinθ)` if θ = 30°
उत्तर
θ = 30°
`((1 - cosθ)(1 + cosθ))/((1 - sinθ)(1 + sinθ)`
= `(1 - cos^2θ)/(1 - sin^2 θ)`
= `(1 - cos^2 30°)/(1 - sin^2 30°)`
= `(1 - (sqrt(3)/2)^2)/(1 - (1/2)^2`
= `( 1 - 3/4)/(1 - 1/4)`
= `(1/4)/(3/4)`
= `(1)/(3)`.
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