Advertisements
Advertisements
Question
What is the value of 9cot2 θ − 9cosec2 θ?
Advertisements
Solution
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
RELATED QUESTIONS
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
`sin^2 theta + 1/((1+tan^2 theta))=1`
`sec theta (1- sin theta )( sec theta + tan theta )=1`
`(cos^3 theta +sin^3 theta)/(cos theta + sin theta) + (cos ^3 theta - sin^3 theta)/(cos theta - sin theta) = 2`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
If sec θ = `41/40`, then find values of sin θ, cot θ, cosec θ
If cos A + cos2A = 1, then sin2A + sin4 A = ?
