Advertisements
Advertisements
प्रश्न
What is the value of 9cot2 θ − 9cosec2 θ?
Advertisements
उत्तर
We have,
`9 cot^2 θ-9 cosec^2θ= 9(cot ^2θ-cosec^2 θ) `
=` -9(cosec ^2θ-cot θ)`
We know that, `cosec ^2 θ-cot ^2 θ-1`
Therefore,
\[9 \cot^2 \theta - 9 {cosec}^2 \theta = - 9\]
APPEARS IN
संबंधित प्रश्न
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
`sin^2 theta + 1/((1+tan^2 theta))=1`
If x= a sec `theta + b tan theta and y = a tan theta + b sec theta ,"prove that" (x^2 - y^2 )=(a^2 -b^2)`
If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.
If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a2 + b2 =
If cos A + cos2 A = 1, then sin2 A + sin4 A =
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
Prove the following identity :
`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
sin4A – cos4A = 1 – 2cos2A. For proof of this complete the activity given below.
Activity:
L.H.S. = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` ...`[sin^2"A" + square = 1]`
= `square` – cos2A ...[sin2A = 1 – cos2A]
= `square`
= R.H.S.
Prove that cot2θ – tan2θ = cosec2θ – sec2θ.
sec θ when expressed in term of cot θ, is equal to ______.
