Advertisements
Advertisements
प्रश्न
Which is not correct formula?
विकल्प
1 + tan2θ = sec2θ
1 + sec2θ = tan2θ
cosec2θ – cot2θ = 1
sin2θ + cos2θ = 1
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
If sin θ + cos θ = x, prove that `sin^6 theta + cos^6 theta = (4- 3(x^2 - 1)^2)/4`
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
If m = ` ( cos theta - sin theta ) and n = ( cos theta + sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
If \[\sin \theta = \frac{1}{3}\] then find the value of 9tan2 θ + 9.
\[\frac{x^2 - 1}{2x}\] is equal to
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Prove the following identity :
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
sec θ when expressed in term of cot θ, is equal to ______.
