Advertisements
Advertisements
प्रश्न
`(cos^3 theta +sin^3 theta)/(cos theta + sin theta) + (cos ^3 theta - sin^3 theta)/(cos theta - sin theta) = 2`
उत्तर
LHS= `(cos^3 theta +sin^3 theta)/(cos theta + sin theta) + (cos ^3 theta - sin^3 theta)/(cos theta - sin theta) `
=` ((cos theta + sin theta)(cos^2 theta- cos theta sin theta + sin^2 theta))/((cos theta + sin theta)) + ((cos theta - sin theta )(cos^2 theta+ cos theta sin theta + sin^2 theta))/((cos theta - sin theta))`
=` (cos^2 theta + sin ^2 theta - cos theta sin theta ) + ( cos^2 theta + sin^2 theta + cos theta sin theta)`
=`(1- cos theta sin theta) +( 1+ cos theta sin theta)`
= 2
= RHS
Hence, LHS = RHS
APPEARS IN
संबंधित प्रश्न
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
`1+(tan^2 theta)/((1+ sec theta))= sec theta`
`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn
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"))` = cosec A + cot A
`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is ______.
