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प्रश्न
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
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उत्तर
cosec4 A (1 – cos4 A) – 2 cot2 A
= cosec4 A (1 – cos2 A) (1 + cos2 A) – 2 cot2 A
= cosec4 A (sin2 A) (1 + cos2 A) – 2 cot2 A
= cosec2 A (1 + cos2 A) – 2 cot2 A
= `cosec^2A + cos^2A/sin^2A - 2cot^2A `
= cosec2 A + cot2 A – 2 cot2 A
= cosec2 A – cot2 A
= 1
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संबंधित प्रश्न
Prove the following trigonometric identities.
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Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
If `sec theta = x ,"write the value of tan" theta`.
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S. = `square`
= `square/(sinθ) + (sinθ)/(cosθ)`
= `(cos^2θ + sin^2θ)/square`
= `1/(sinθ.cosθ)` ...`[cos^2θ + sin^2θ = square]`
= `1/(sinθ) xx 1/square`
= `square`
= R.H.S.
Eliminate θ if x = r cosθ and y = r sinθ.
