Advertisements
Advertisements
प्रश्न
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
उत्तर
LHS = `cosec^4A - cosec^2A`
= `cosec^2A(cosec^2A - 1)`
RHS = `cot^4A + cot^2A`
= `cot^2A(cot^2A + 1)`
= `(cosec^2A - 1)cosec^2A`
Thus , LHS = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
sin2 A cot2 A + cos2 A tan2 A = 1
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
Prove that:
`cosA/(1 + sinA) = secA - tanA`
Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`
Write the value of tan10° tan 20° tan 70° tan 80° .
Write the value of tan1° tan 2° ........ tan 89° .
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Find the value of sin 30° + cos 60°.
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
Show that `(cos^2(45^circ + theta) + cos^2(45^circ - theta))/(tan(60^circ + theta) tan(30^circ - theta))` = 1
