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प्रश्न
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
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उत्तर
Sin4θ – cos4θ = 1 – 2cos2θ
LHS = Sin4θ – cos4θ
LHS = (Sin2θ)2 – (cos2θ)2
LHS = (Sin2θ + cos2θ)(Sin2θ - cos2θ) ...[a2 – b2 = (a + b)(a – b)]
LHS = (Sin2θ – cos2θ).(1) ...(Sin2θ + cos2θ = 1)
LHS = 1 – cos2θ – cos2θ ...(1 – Sin2θ = cos2θ)
LHS = 1 – 2cos2θ
RHS = 1 – 2cos2θ
LHS = RHS
Hence proved.
संबंधित प्रश्न
Prove that `cosA/(1+sinA) + tan A = secA`
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Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
If sec θ + tan θ = x, then sec θ =
sec4 A − sec2 A is equal to
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sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove the following identity :
`(1 + sinA)/(1 - sinA) = (cosecA + 1)/(cosecA - 1)`
Prove the following identity :
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Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
If sec θ = `25/7`, then find the value of tan θ.
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Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
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If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
