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प्रश्न
(sec2 θ – 1) (cosec2 θ – 1) is equal to ______.
पर्याय
–1
1
0
2
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उत्तर
(sec2 θ – 1) (cosec2 θ – 1) is equal to 1.
Explanation:
(sec2 θ – 1) (cosec2 θ – 1) = tan2 θ.cot2 θ ...`[(∵ sec^2 θ - 1 = tan^2 θ),("cosec"^2 θ - 1 = cot^2 θ)]`
= `tan^2 θ . 1/tan^2 θ`
= 1
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संबंधित प्रश्न
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sec2 A . cosec2 A = tan2 A + cot2 A + 2
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`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
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Activity:
L.H.S = `square`
= `cos^2theta xx square .....[1 + tan^2theta = square]`
= `(cos theta xx square)^2`
= 12
= 1
= R.H.S
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