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प्रश्न
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following:
(sec2 θ − 1) (cosec2 θ − 1) = 1
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उत्तर
We know that
sec2 θ − tan2 θ = 1
cosec2 θ − cot2 θ = 1
So,
(sec2 θ − 1)(cosec2 θ − 1) = tan2 θ × cot2 θ
= (tan θ × cot θ)
= `(tan θ xx 1/tan θ)^2`
= (1)2
= 1
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