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
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
Prove the following trigonometric identities.
`sin theta/(1 - cos theta) = cosec theta + cot theta`
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Show that : tan 10° tan 15° tan 75° tan 80° = 1
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
`cot^2 theta - 1/(sin^2 theta ) = -1`a
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
Write the value of `(1 + tan^2 theta ) cos^2 theta`.
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
If sin θ + cos θ = `sqrt(3)`, then show that tan θ + cot θ = 1
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
Show that, cotθ + tanθ = cosecθ × secθ
Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
