Advertisements
Advertisements
प्रश्न
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
उत्तर
L.H.S. = (cos A + sin A)2 + (cos A – sin A)2
= cos2 A + sin2 A + 2 cos A . sin A + cos2 A + sin2 A – 2 cos A . sin A
= 2 sin2 A + 2 cos2 A
= 2(sin2 A + cos2 A) ...(∵ sin2 A + cos2 A = 1)
= 2 × 1
= 2
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 - sin theta)/(1 + sin theta) = (sec theta - tan theta)^2`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
If sin θ − cos θ = 0 then the value of sin4θ + cos4θ
Prove the following identity :
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
Prove the following identity :
`((1 + tan^2A)cotA)/(cosec^2A) = tanA`
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.
