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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
संबंधित प्रश्न
Prove the following trigonometric identities.
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`sinA/(1 - cosA) - cotA = cosecA`
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`(sin^2θ)/(cosθ) + cosθ = secθ`
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
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`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
