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प्रश्न
Which is not correct formula?
विकल्प
1 + tan2θ = sec2θ
1 + sec2θ = tan2θ
cosec2θ – cot2θ = 1
sin2θ + cos2θ = 1
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उत्तर
1 + sec2θ = tan2θ
Explanation:
(A) 1 + tan2θ = sec2θ: Correct. This is a fundamental Pythagorean identity.
(B) 1 + sec2θ = tan2θ: Incorrect. Rearranging the correct identity from (A) gives sec2θ – 1 = tan2θ.
(C) cosec2θ – cot2θ = 1: Correct. This is derived from the standard identity 1 + cot2θ = cosec2θ.
(D) sin2θ + cos2θ = 1: Correct. This is the primary Pythagorean trigonometric identity.
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संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
Prove the following trigonometric identities.
`(tan^2 A)/(1 + tan^2 A) + (cot^2 A)/(1 + cot^2 A) = 1`
Prove the following trigonometric identities.
`(1 + cos θ + sin θ)/(1 + cos θ - sin θ) = (1 + sin θ)/cos θ`
Prove the following identities:
sec2A + cosec2A = sec2A . cosec2A
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
`cosec theta (1+costheta)(cosectheta - cot theta )=1`
Write the value of tan10° tan 20° tan 70° tan 80° .
If `sec theta + tan theta = x," find the value of " sec theta`
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Prove the following identity :
`(cos^3θ + sin^3θ)/(cosθ + sinθ) + (cos^3θ - sin^3θ)/(cosθ - sinθ) = 2`
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
Prove that sin4θ - cos4θ = sin2θ - cos2θ
= 2sin2θ - 1
= 1 - 2 cos2θ
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
If `1 - cos^2θ = 1/4`, then θ = ?
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
